Jansman 2017

Hellendoorn, May 2017

Additive manufacturing as a solution for supply obsolescence

by Jorn Jansman

BSc. Industrial Engineering and Management – University of Twente 2014 Student Identity number 0919940

in partial fulfilment of the requirements for the degree of Master of Science in Operations Management and Logistics

Supervisors: Dr. Ir. R.J.I. Basten, TU/e, OPAC Ir. B. Westerweel, TU/e, OPAC Prof. Dr. Ir. G.J.J.A.N. van Houtum, TU/e, OPAC Ir. K. Alizadeh, Company supervisor

Keywords: Additive Manufacturing, 3D printing, obsolescence management, last time buy, final order

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Abstract Additive Manufacturing (AM) is a production technique that is associated with low setup times and low setup costs, and it is therefore relatively inexpensive for small-series production. This makes that AM has a great potential in the spare-parts supply chain. A special case is the obsolescence case, when spare parts are not available due to discontinued production at the original equipment manufacturer.

In this thesis, we research if AM is a solution for obsolescence problems at an aerospace services provider.

We do this by making three models. The AM suitability model determines if a part can be produced with AM. The production cost model estimates the costs for making a part with additive manufacturing, which can be used as input for the third model. In this last time buy model, we determine a sourcing strategy for nearly obsolete parts. For these parts, we consider three sourcing options, the last time buy, the secondhand market, and additive manufacturing, and in the model, we determine the combination of these options that minimizes the total expected costs over the remaining life cycle.

With these models, we perform two case studies. In both cases, AM is not part of the optimal sourcing strategy. We find that the costs related to the airworthiness certification of AM parts are too high. The logistical benefits of AM over the remaining life-cycle are not enough to compensate for the certification costs.

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Management Summary Additive Manufacturing (AM), or 3D-printing, is a relatively new production technique that is especially suitable for making parts with complex geometries in small production volumes. This research is performed at an aviation services company, to which we refer as The Company (TC). The TC is interested in using AM to produce obsolete, or nearly obsolete parts. These are parts that are, or will become difficult to source because the Original Equipment Manufacturer (OEM) has ceased, or is going to cease, normal production. A reason for the OEM to stop production can be that tools, such as molds, are no longer available. Another reason can be that, due to the limited production volume, it is no longer economically interesting to produce the parts. TC needs to find a different way to source these nearly obsolete parts. In this thesis, it is investigated if AM is a solution for this problem. This project is part of the larger SINTAS (Sustainability Impact of New Technologies on After Sales service supply chains) research project. In the SINTAS project, many aspects of AM are investigated, for instance the effect on the supply chain network design of placing AM production capacity close to customers. In this Master thesis project, however, we focus on the obsolescence problem, in a situation where AM production is outsourced to an AM service provider. We focus on nearly obsolete parts. These are parts for which TC should make a Last-Time-Buy (LTB) decision.

This project is split in the following three parts: Which items are feasible to produce with AM? We have developed an AM suitability model, in which it can be determined if a part can be produced with AM. With this model, a part that has the risk of becoming obsolete, can be quickly analyzed. The model advices not only on the suitability for AM, but also on the preferred AM production process and material.

In the model, we limit the number of materials to a total of seven, of which four are plastics, and three are metals. These are all-round materials, that can be used for many different parts. By limiting the number of AM materials, it is easier to assess the quality of the AM parts, which is important, because the AM parts need to be certified for airworthiness. The airworthiness certification is a process which takes place at TC, and requires engineers to ensure the quality of a part. In this certification process, there are recurring costs related to the part, and non-recurring costs related to the AM material. By limiting the number of AM materials, the recurring costs for certification are limited. Whenever TC has gained a high amount of experience with these materials, it can choose to research other AM materials for other (specialized) applications.

What are the costs of producing with AM? The costs of AM can be split in fixed development costs and variable production costs. We have developed a production cost model, in which the variable production costs of a part can be determined based on material and size of a part. We find that the variable production costs of AM are generally higher than those of conventionally produced parts. Especially metal parts are significantly more expensive, although the difference becomes smaller when production volumes decline. Producing with AM is more expensive than conventional production because of expensive machines, expensive raw materials and extra postprocessing costs that apply for AM parts. The fixed development costs are the costs for making new designs for AM, and certifying the part for aviation. Because AM is a new production technique, with which TC has no experience, the certification process becomes very expensive.

For a small plastic part, with little strength requirements, it is expected that 200 engineering hours are needed for the certification process. This translates to an investment of around â‚Ź20,000. From these 200

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hours, approximately 50 are non-recurring, which means that they do not apply for a different part that is produced in the same AM material.

For metal parts, or parts with higher strength requirements, the certification costs are expected to be a factor two higher than for plastic parts. The main concern in the certification process is the reproducibility of AM, which means the capability to produce the same part with the same mechanical properties over different production runs. While at the moment the certification costs are very high, it is expected that these costs decline in the future, because the quality of AM parts will increase when the technology improves.

What is the cost optimal decision when considering multiple options for spare parts acquisition of nearly obsolete parts?

The variable production costs of AM parts are most often higher than those of conventionally produced parts. However, using AM has logistical benefits over using conventional production techniques, especially when it comes to nearly obsolete parts, for which TC should make a Last-Time-Buy (LTB) decision. Two of the logistical advantages of AM are the short setup time, and the possibility for small series production.

With these properties, it is possible to produce on demand, which greatly reduces inventory holding costs.

Furthermore, with on demand production, it is not necessary to make detailed demand predictions. Due to this, using AM may result in lower costs over the entire life-cycle of the parts.

In this thesis, we develop a last time buy model that minimizes the total life-cycle costs based on the three alternative sourcing options, the LTB, the second-hand market (SH) and AM. All these options have benefits and drawbacks. The LTB often has the lowest part costs, but requires a big up-front investment and long-term demand prediction. SH does not require a high investment, but the supply of SH parts can be limited. Therefore, extra safety stock is required, and it is necessary to make predictions on both supply and demand. AM can be used for on-demand production, but requires a big investment in development and certification. Furthermore, the variable part costs are often higher than for the alternatives.

With the last time buy model, we perform two case studies, one for an inexpensive plastic part, the other for an expensive metal part. In both cases, AM turns out not to be part of the best sourcing strategy, which is mainly due to the high development costs. For the plastic part, the development cost should reduce with almost a factor 10 compared to the current estimated costs. In that case, the costs of an LTB and AM are equal. However, another factor in determining the best strategy is the robustness of the costs relative to changes in demand. Especially when demand is higher than expected, the costs for AM are much more robust than the LTB-costs. This is because AM can scale up production, while the LTB is fixed, and expensive alternatives are needed when demand is higher than the LTB. The second part we analyze is an expensive metal part, with a relatively high demand. This part has a limited available supply on the second-hand market (SH). The result of the model is that a combination of the LTB with SH results in the lowest costs. When we do not consider SH, the lowest expected costs are found with a combination of the LTB with AM, which means that the LTB is used to cover demand in the first periods, after which AM is used to cover the demand in the final periods. Such a strategy reduces the up-front investment and holding costs for the LTB.

Conclusions Within this thesis, we investigate if AM is a solution for obsolescence problems at The Company. We conclude that AM has the technical capabilities to produce spare parts for aviation, but, at the moment,

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certification of AM parts is too expensive. When the certification costs decline, AM can save costs in obsolescence cases, because AM is suitable for small production volumes, with low setup times, and thus short lead times. This results in lower costs over the entire remaining life-cycle, because inventory holding costs decline, and because production can be done on demand, which means there is no need to make a detailed demand prediction.

The certification costs are expected to decline when aviation authorities recognize AM as an accepted production technique. One of the most important issues that has to be solved, before AM will be accepted, is the reproducibility of AM machines. Reproducibility is the ability of an AM machine to produce the same part with the same properties over different production runs. Outside of the aviation industries, where certification costs may not apply, the potential for AM is higher. Specific price differences and lead times between conventional, second-hand market and AM determine if AM reduces costs. In the two case studies we made, reducing the AM certification costs to zero, resulted in one positive business case for AM. In the other case, where the second-hand market is cheaper than AM, reducing certification costs did not result in a positive business case.

In most literature on AM it is stated that AM has a high potential for slow-moving parts, but in this research, we conclude that in last time buy situations, due to the development and certification cost, the potential of AM is higher for parts with a higher demand. Furthermore, with increased demand, uncertainty increases and the benefit of on demand production becomes larger. In other industries, where certification costs do not apply, AM can also be interesting for lower demand volumes.

Recommendations When the certification costs decline, AM has the potential to be a solution for obsolescence problems.

However, at this point in time, it is too expensive compared to conventional manufacturing and secondhand supply. This is mainly due to the high development costs related to the certification process. TC should research if and how the certification of AM parts can be improved. In this process, TC should cooperate with AM machine manufacturers, and the aviation authorities. The machine manufacturers have to convince the aviation authorities of the quality and reproducibility of products from their machines. When this is the case, the AM process can be certified, instead of each individual part. This drastically reduces the AM development costs, and can result in a wider application of AM within TC. Another important step in AM research is to select a demonstrator part. With this part, TC should go through the entire certification process. This does not need to be a financially positive business case, because it should be considered as a learning case. Such a demonstrator will increase the knowledge of AM at TC, and can be the start for finding other applications for AM, outside of obsolescence problems.

The AM suitability model developed in this thesis can be used to make a quick technical assessment of potential demonstrator parts. With the production cost model, the variable production costs can be estimated. Finally, with the LTB model, the life-cycle costs of the demonstrator can be compared with the alternative, which gives better insight in the total investment costs. If it is not possible to select and produce a demonstrator part, another possibility may be to not print the part itself, but to print the tooling instead. When the tooling is printed and not the part, the certification process is less expensive, because the qualifications for tooling are less strict. Therefore, it will be easier to make positive business cases for AM. To use the option of printing the tooling, TC has to research the qualifications for the tooling, and research which AM process and material can be used to produce the tooling.

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Contents Abstract ........................................................................................................................................................ III Management Summary ................................................................................................................................ IV Introduction ........................................................................................................................................... 1 Company description..................................................................................................................... 1 Obsolescence at The Company ..................................................................................................... 1 Additive manufacturing ................................................................................................................. 2 SINTAS research project ................................................................................................................ 3 Project design ........................................................................................................................................ 4 Problem definition......................................................................................................................... 4 Research questions........................................................................................................................ 4 Scope ............................................................................................................................................. 6 Contributions to science and industry .......................................................................................... 6 Report layout ................................................................................................................................. 8 Additive Manufacturing feasibility ........................................................................................................ 9 AM technology .............................................................................................................................. 9 Limitations of AM ........................................................................................................................ 10 AM suitability model ................................................................................................................... 12 Additive Manufacturing costs ............................................................................................................. 15 AM cost factors............................................................................................................................ 15 Machine and build time calculation ............................................................................................ 19 Validation .................................................................................................................................... 21 Spare parts acquisition after end of production ................................................................................. 22 Last time buy model .................................................................................................................... 22 Evaluation .................................................................................................................................... 25 Optimization ................................................................................................................................ 33 Relation to literature ................................................................................................................... 34 Model limitations ........................................................................................................................ 35 Business cases ..................................................................................................................................... 36 Ceiling bracket ............................................................................................................................. 36 Skid .............................................................................................................................................. 42 Conclusion case studies ............................................................................................................... 48 Conclusions and recommendations .................................................................................................... 49

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Conclusions.................................................................................................................................. 49 Recommendations....................................................................................................................... 50 References ................................................................................................................................................... 52 Appendix A: Obsolescence solutions at TC ................................................................................................. 55 Appendix B: Decision Tree AM .................................................................................................................... 57 Appendix C: Aviation Certification .............................................................................................................. 58 Appendix D: AM cost model ........................................................................................................................ 59 Appendix E: certification hours ceiling bracket ........................................................................................... 60

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Introduction This master thesis describes a project in which the use of additive manufacturing at an aviation services company is researched. For reasons of confidentiality we refer to The Company when we mention the aviation services company. The project focuses on obsolescence problems, when parts cannot be supplied due to discontinued production. In this chapter, we introduce The Company, which considers Additive Manufacturing (AM) as an alternative sourcing when parts become obsolete. Furthermore, we give an introduction to additive manufacturing and the SINTAS research project. Chapter 2 follows with the problem definition and research design. At the end of Chapter 2 we introduce the rest of this thesis.

Company description In the early years of the 20th century The Company began building aircraft, and quickly became one of the largest aircraft manufacturer worldwide. During the decades that followed, The Company built many aircraft, both for military and commercial customers.

The Company (from now: TC) started as the maintenance organization for its fleet of aircraft. During the years, TC expanded its capabilities, and now also supports other aircraft types. This research is performed at the services department of the company, which aims to minimize downtime for aircraft operators by providing spare parts, and doing repairs on aircraft components. The Company keeps a stock of over 120,000 different part numbers. This stock is kept in three warehouses, which are located in three different continents.

Obsolescence at The Company For a limited number of aircraft types, TC provides total support solutions. This means The Company fulfills all customer requests for maintenance and spare parts. Among these aircraft are the companies’ aircraft, which are no longer in production. The moment production of the aircraft stops is called End of Production (EOP). After this moment, service for the aircraft is guaranteed until the End of Service (EOS). The time between EOP and EOS is called the End of Life (EOL). This is shown in Figure 1.1.

Figure 1.1: End of Life

During the EOL, demand for spare parts declines, because the installed base size declines. This increases the risk of obsolescence of spare parts, both on the supply side and on the inventory side. In this project, we focus on supply obsolescence, for which we use the following definition (Li et al, 2016):

Obsolescence is the non-availability of parts due to discontinued production.

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Because obsolescence is a recurring problem, TC has already done an extensive amount of work to improve its performance. For obsolete, or nearly obsolete parts, TC has designed a procedure that considers seven options sequentially. This is shown in Figure 2.1:

1. Last time buy

2. Secondhand market

3.

Resourcing

4. Development of PMA

7. Redesign of System

6. Redesign of Part

5. Development of repair

Figure 1.2: Obsolescence procedure at The Company

The last time buy is in most cases the preferred option, because it has the lowest costs per part. The disadvantage of the LTB is that it requires a big up-front investment, and due to the stochastic nature of spare parts demand, TC runs the risk of either buying too many parts, or running out of parts before the EOS. Therefore, it can in some cases be better to use the second-hand market, or to find a different supplier (resourcing). These options reduce the up-front investment, and can be better in cases of uncertain demand. Furthermore, the original equipment manufacturer (OEM) does not always give notice to TC that it discontinues production. In these cases, an LTB is not possible and TC has to find an alternative supply mode.

The options 4-7 are methods to repair or produce a new part with the same functionality, either in house or outsourced. These options require more investments and are therefore not preferred. Appendix A shows a description of all the options, and shows how often each of the options is used during the period 2007-2014.

Additive manufacturing Additive manufacturing (AM), also known as 3D printing, is a promising new production technique. The process of AM is additive, meaning material is added during the building process, rather than removed, as in many other production techniques, such as milling.

Whereas in its early years AM was mainly used for making prototypes, it has now developed into a production technique for usable, including metal, parts. Production with AM can have a number of benefits for industry, for example, the design of parts is not limited by the production technique. The shape of parts can be as complex as imaginable (Comb, 2010), without making production significantly slower or more expensive. Another advantage is that there are no high setup costs associated with starting an AM production run, which makes production in low volumes economically viable.

Combined with the low lead times of AM, this makes it possible to produce parts on demand, which is very interesting in the after-sales service supply chain. Inventories can become significantly lower, while retaining high service levels. In a future scenario, it could even become possible that 3D printers are

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located at the installed base of the capital goods. In this case, the OEM can send drawings to the customers, who can then print parts on demand.

Disadvantages of AM can be the limited availability of materials, and the potentially lower quality of parts produced with AM. Next to that, AM machines are expensive, so a high utilization is needed to make the investment worthwhile. An alternative is to outsource AM production to an AM service provider.

Furthermore, in the aviation industry, airworthiness certification of AM parts can be a significant cost factor that can limit the use of AM. Despite the disadvantages, many companies and research institutes have recognized the potential of AM, and are looking to increase knowledge on not only technical possibilities, but also the logistical impact of AM. One of these projects is the SINTAS research project, which is described in Section 1.4.

SINTAS research project This thesis project is part of the SINTAS (Sustainability Impact of New Technologies on After-sales Service supply chains) research project. In this project the Eindhoven University of Technology and the University of Twente collaborate with several industry partners to research if and how AM can influence service supply chains.

The project consists of three Work Packages (WP’s). WP1 consists of mainly technical capabilities of AM. WP2 looks into the effect of AM on the after-sales service supply chain: when AM costs decline, it may be possible to deploy AM machines close to the customers. In this way, the number of echelons in the supply chain can be reduced. This leads to shorter lead times. WP3 researches, given the network design from WP2, the impact of AM on the logistics processes. This can be a reduction of spare parts inventory, or a decrease in obsolescence problems. Other effects can be more efficient transportation and a reduction of pollution as a result. Given the interests of TC, this thesis project fits best with WP3, with links to WP1 (technical requirements) and WP2 (network design). The main research questions of WP3 are: 1. How will spare part inventory levels be influenced in the various stages of the asset life cycle as consequence of the use of 3D printing, proceeding from the supply chain design (WP2), the component failure behavior (WP1) and the modified maintenance requirements (WP1)?

2. For which type of parts may we expect the highest impact on sustainability in terms of obsolescence reduction?

3. What is the impact of the use of 3D printing on (emergency) transportation in the supply chain, and for which types of components can we expect most sustainability impact in this respect?

This thesis project will contribute to Research Questions 1 and 2. It can give important insights into the application of AM in industry.

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Project design This chapter introduces the obsolescence problem found at The Company in Section 2.1. Based on the problem definition, the research model and research questions follow in Section 2.2. We limit our research to a number of points, which are explained in Section 2.3. In Section 2.4 we show how this thesis can contribute to scientific and industrial knowledge on AM and Section 2.5 gives a short introduction to the next chapters of this thesis.

Problem definition A big part of the spare parts deliveries at TC is related to aircraft that are out of production. TC guarantees the support for these aircraft until at least 2030, and thus has to make sure that spare parts are available.

In the case that parts become obsolete, TC has to find an alternative way to acquire them. Given that AM is a production technique with low setup times, and is economically feasible for small series, it is a promising solution for obsolescence. Therefore, we define the research problem as follows:

Is AM a solution for obsolescence problems at TC?

TC has already started to research AM by collaborating in the SINTAS project. As part of this project, Sterkman (2015) explored the opportunities for using AM at TC. Sterkman set up a list of mainly economic criteria, such as demand, price and inventory turnover rate, that can be used to score parts on AM potential. To incorporate technical feasibility, he used indicative criteria. Parts that receive a high score need to be manually checked, on both technical and economic feasibility. The goal of our project is to evaluate this technical and economic feasibility of AM.

Research questions Based on the problem definition in Section 2.1, the main research question of this project is as follows:

Under what criteria can AM be a solution to obsolescence problems in the aviation industry, and how does the AM solution compare to other obsolescence solutions?

The criteria needed to determine if AM can be used in the aviation industry are mostly technical. This question is left open by Sterkman, who only gives a number of indicative criteria. Therefore, we develop a structural way to assess technical feasibility for AM. To compare AM with other sourcing options, we need an estimation of the production costs of AM. These can, together with inputs on demand forecast, and parameters of other sourcing options, be used to determine the optimal sourcing strategy for nearly obsolete parts, for which it is possible to make a last time buy. We illustrate this with two studies in the final part of this thesis. This process is illustrated in the research model in Figure 2.1.

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Figure 2.1: Research questions

The research questions corresponding to Figure 2.1 are as follows: 1. Which items are feasible to produce with AM? In order to answer this research question, we set up technical criteria to asses if parts can be produced with AM. This is based on online information of AM machine manufacturers, such as Stratasys, EOS, and SLM solutions. Next to that, interviews are conducted at Additive Industries, another AM machine manufacturer, and Materialise, an AM service provider. The criteria are implemented in a decision tree that can be used at TC. 2. What are costs of producing with AM? With this research question we analyze the costs of AM. The costs of AM consist of fixed development costs, and variable production costs. The variable production costs can be divided in direct costs, such as material costs, and indirect costs, such as machine costs. The result of this research question is implemented in an Excel sheet that calculates total costs based on part dimensions, material, and AM process. This is based on interviews at Additive Industries and Materialise, and online information of AM machine manufacturers.

3. What is the cost optimal decision when considering multiple options for spare parts acquisition of nearly obsolete parts?

To answer this research question, we develop a mathematical model for the spare parts acquisition at TC. As we have seen in Section 2.1, TC considers multiple options in case of (future) obsolescence, such as the last time buy, second-hand market, and multiple forms of alternative production. AM can be a production method that can significantly influence the way in which TC deals with obsolescence, because it is potentially cheap for small production volumes, and production can be made on demand. This has the advantage that the demand uncertainty is less important, opposed to the last time buy, where there is a risk of buying too few, or too many parts. To answer this research question we use literature on spare parts acquisition for obsolescence, such as Inderfurth and Kleber (2013) and Wullms (2014). Their models resemble the situation of TC, but needs to be adapted to be able to also consider AM as an obsolescence solution.

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4. Can AM be used to save costs in the case of obsolescence?

With this final research question, we investigate a number of parts with the results from the previous research questions. The parts are tested on technical feasibility, part costs and the final order decision.

The parts we analyze are part of the parts catalogue of TC. For these parts, data on demand, material and other specifications are available in the ERP system of TC. With the results of these case studies we can conclude if AM is a cost-effective solution for obsolescence.

Scope We limit our research on a number of areas. In assessing if a part can be printed, we focus on technology that is currently available. This means we do not speculate on improvements in AM. When the technology does improve, for instance bigger parts can be built, it should be easy for TC to adjust the relevant parameters in the models.

We also do not consider intellectual property of drawings, because we focus on proprietary parts, which means that TC is owner of the designs of these parts. Another assumption we make, is that AM parts have the same mechanical properties and failure rates as the originally manufactured parts. This is a precondition that needs to be fulfilled to get permission to use the part in the aviation industry. As long as this is not true, use of AM in aviation will be very limited.

In evaluating life time costs of the various options, we use a single location model. This is a valid assumption for TC, because TC wants to outsource AM production, and make quality checks at the main warehouse.

Finally, we limit the number of obsolescence solutions considered to three: the LTB, the second-hand market, and AM. The other options that TC considers are permanent solutions; if TC chooses one of these options, it is not necessary to also consider AM.

Contributions to science and industry The interest from science and industry in AM is high. In this section, we show how this thesis adds to the knowledge of AM and its impact on service supply chains, both from a scientific and an industry perspective.

2.4.1 Science Since AM is a relatively new production technique, there are only few articles describing its impact on supply chains. Westerweel et al. (2016) describe under which circumstances it becomes feasible for an OEM to design and produce a part with AM instead of conventional production techniques. The AM and conventional part will have different development costs, production costs, production lead times and reliability. The model of Westerweel et al. evaluates the life-cycle costs of both options, and based on those costs the OEM can make a decision on which production technique it wants to use.

Because our research focuses on last time buy situations, we evaluate the literature on this topic. The last buy problem is a well-known problem in scientific literature. There are many articles that describe the optimal last buy, in combination with other sourcing options. Behfard et al. (2015) give an overview of articles on this problem, with the solutions they consider. This is shown in Table 2.1.

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From this list, we are mainly interested in the articles that describe three options; these are Inderfurth and Mukherjee (2008), Inderfurth and Kleber (2013), and Krikke and Van der Laan (2011). The articles of Inderfurth are the most interesting with respect to our case, because they consider options very similar to the options at TC. Inderfurth and Mukherjee propose a dynamic programming approach, for which a heuristic method is developed by Inderfurth and Kleber. They recommend to research other alternative sourcing options to extend their model. AM can be such an option. These articles are reviewed in depth in the literature review by Jansman (2016).

Table 2.1: LTB literature (Behfard et al. 2015) LTB

Repair of failed parts

Retrieve parts from dismantling

Perform extra production runs

Moore (1971)

x

Ritchie and Wilcox (1977)

x

Fortuin (1980)

x

Fortuin (1981)

x

Klein Haneveld and Teunter (1998)

x

Hong, et al. (2008)

x

Leifker, et al. (2012, 2014)

x

Teunter and Fortuin (1998)

x

x

Teunter and Fortuin (1999)

x

x

Kleber et al. (2012)

x

x

Inderfurth and Mukherjee (2008)

x

x

x

Inderfurth and Kleber (2013)

x

x

x

Pourakbar et al. (2014)

x

x

Teunter and Klein Haneveld (2002)

x

Krikke and Van der Laan (2011)

x

x

Van Kooten and Tan (2009)

x

x

External market

x x

The combination of a last buy and AM is researched in the master thesis project of Wullms (20014), who develops a model that combines the last buy and AM. Wullms concludes that AM can lead to a decrease in the last buy quantity, because AM is used to cover the uncertain demand in the final phase. The difference between our model and the model of Wullms, is that we also consider the option of secondhand market for spare parts. Furthermore, we add the property that demand declines over time, where Wullms considers stable demand.

Other interesting master thesis projects are conducted by Zanders (2009) and Abbink (2015). Zanders (2009) researches the LTB in combination with two other sourcing options. Abbink (2015) researches the impact of AM on service supply chains. The combination of options that we consider has not yet been researched so far, which makes that this thesis contributes to the scientific knowledge on last buy problems, and the logistical impact of AM.

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2.4.2 Industry Obsolescence is a common problem for capital goods with long lifetimes, such as aircraft, automobiles and trains. These kind of capital goods typically have many parts that can be produced with AM, which makes that many manufacturers show interest in using AM as an obsolescence solution. In this project, we make a simple AM suitability model that can be used to make a basic technical assessment of AM feasibility of a part. Next to that, an AM production costs model is developed. Both the suitability model and the production cost model are developed for today’s technology, but can be easily adapted when technology improves. The last time buy model developed in this thesis is very useful when companies notice that a part may become obsolete in the future, and consider using AM to solve this obsolescence.

2.4.3 Deliverables Each of the research questions in this thesis forms the basis for a deliverable at TC, which means the deliverables are: • • • •

Decision trees for assessing technical feasibility Model to estimate AM production costs Model to optimize spare parts acquisition for (nearly) obsolete parts Business cases to illustrate the cost effects of AM

Report layout The next chapters of this thesis cover each one of the research questions formulated in Section 2.2. That is, Chapter 3 describes AM feasibility, Chapter 4 shows a way to estimate AM production costs, and in Chapter 5 we describe a mathematical model for spare parts acquisition of nearly obsolete parts. In Chapter 6 we use the results of the previous chapters to make business cases for a number of spare parts from TC. Finally, in Chapter 7 we show the conclusions and recommendations.

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Additive Manufacturing feasibility In this chapter we answer Research Question 1: Which items are feasible to produce with AM? To answer this question, we look at the limitations of AM as a production technique. These limitations are different for each AM process. Section 3.1 explains the relevant AM processes for producing functional parts. In Section 3.2 we look into the limitations and capabilities of the relevant AM processes. These are implemented in a decision tree that checks AM feasibility for parts in Section 3.3.

AM technology There is a wide range of AM technologies. In this section, we focus on two processes that can be used to produce parts for the aviation industry. These processes are Fused Deposition Modelling (FDM) and Powder Bed Fusion. Other AM processes are more suitable for rapid prototyping; for a description of the other processes we refer to Wullms (2014).

Fused Deposition Modelling is a material extrusion technique.

A thermoplastic material is fed through a material spool. In the extrusion head this material is heated to its melting point, after which it is selectively deposited on the build platform. This process requires support structures, that are printed simultaneously, and need to be removed during post processing. This is a relatively simple process that does not require extensive training for operators. The FDM process is shown in Figure 3.1.

Figure 3.1: Fused Deposition Modelling (Custom Part Net, 2008)

Powder Bed Fusion is the name for a group of processes based around the same principle. Techniques grouped under this process are Selective Laser Sintering (SLS), Direct Metal Laser Sintering (DMLS), Selective Laser Melting (SLM), and Electron Beam Melting (EBM). All these processes start with a powdered material. A thin layer of this powder is rolled on the build platform, after which the powder is selectively fused together by an energy source. After one layer the building platform is slightly dropped, after which a new layer of powder is added. This process is shown in Figure 3.2.

Figure 3.2: Powder Bed Fusion (3D Printing Industry, 2016)

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SLS, DMLS, SLM, and EBM are all variations on the powder bed fusion process. However, there are differences. SLS is a technique that can be used for plastics. The powder is sintered together, meaning it is not fully melted, as is the case with the SLM and EBM process. SLS requires less heat, with the advantage that the powder is also the support structure (Stratasys, 2016). With the other techniques, it is possible to produce metal parts. This requires support structures during the build process, due to the heat that builds up during the process (Stratasys, 2016).

Limitations of AM There are certain limitations to AM, which are explained in this section, and implemented in a decision tree, that that can not only be used to determine AM feasibility, but also gives advice on the AM process and material.

3.2.1 Machine limitations Table 3.1 shows a number of basic machine limitations for each of the processes. Here we use an SLM machine to show the characteristics of a typical machine for metal AM. These limitations are technology dependent, and expected to improve in the future.

Table 3.1: Machine limitations (DMRC, 2016; Karunakaran et al., 2012)

Size (XYZ, mm) Minimum wall thickness (mm) Tolerances (mm)

FDM (Stratasys Fortus SLS (EOS P760) 900) 914* 609*914 700*380*580 1.5 1

SLM (EOS M400)

0.13

0.1

0.1

400*400*400 1

3.2.2 Material limitations There is are many materials available for AM, from these materials we have a selection of materials that are relevant for TC. We list basic properties of these materials in Table 3.2. These properties give a good indication of the printability of a part, however for different parts, different properties can be needed to determine printability. For this, expert knowledge of both the part and AM materials is needed.

Table 3.2: Material characteristics (Bagsik et al., 2010; EOS, 2016)

Process

Material

Density g/cm3

FDM

Ultem PA12 PEEK PA12FR Titanium Aluminum Stainless Steel Inconel

1.34 1 1.31 1.06 4.41 2.67 7.9 8.19

SLS SLM

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Ultimate strength XY (MPA) 61 53 90 46 1290 445 640 1000

Ultimate strength Z (MPA) 40 43 * 40 1240 405 540 890

Ultimate strength conventi onal 88 55 96 55 950 450 580 965

Flame retardant

Chemical resistant

X

X X X X X X X X *not listed

X X X X X X

3.2.3 AM certification Another factor that can limit the use of AM in aviation is airworthiness certification. Every part designed for an aircraft needs this certification, and in case the same part is produced with a different production technique, the part needs to be certified again. To do this certification, the values in Table 3.2 are not sufficient, and extensive testing is needed to determine the final strength of the part. A background on this certification process can be found in Appendix C. In case of changing the production technique for a part, engineers need to make sure that the new part has the same properties as the conventionally produced part. Because AM is a new production technique, certification is more difficult. One of the main concerns regarding AM is reproducibility, which is the capability to produce the same part with the same geometrical and mechanical properties over different production runs. There are many variables that can influence this, for instance machine settings such as layer thickness, or outside factors such as temperature or humidity. The certification of AM parts can be very time consuming and thus costly. This means that in the aviation industry AM has a high fixed development costs, which may be less in other industries. In Chapter 6 we analyze certain parts, and also comment on the cost of certification.

3.2.4 Post processing Most parts produced with AM need some kind of post processing. In Table 3.3 the post processing requirements for each of the relevant processes are ranked on a 3-point scale, where 1 indicates a low amount of post processing, and 3 a high amount. This table is based on Gibson et al. (2015).

Table 3.3: AM post processing

Process Support material removal Surface texture improvements Accuracy improvements Aesthetic improvements Property enhancement

FDM 1

SLS 2

SLM 3

2

1

2

2

1

1

2

1

2

1

1

3

The values in Table 3.1 are relative values compared to the other post processing technique. Actual postprocessing times depend on design wishes and the shape complexity of the part, and are therefore not generalizable. The total post processing time can range from several minutes for an FDM part, to several hours for a metal part that needs thermal post processing.

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AM suitability model In this chapter, we look into AM processes, AM materials, and certification issues for the aviation industry.

The identified factors are used to construct a decision tree that can be used to decide if a part can be produced with AM, and in which material it should be printed.

3.3.1 Decision tree plastic Figure 3.3 shows the decision tree for plastic parts, this does not consider the actual shape of the part, because AM can produce at least the same geometrical complexity as normal production processes.

However, some processes and geometries need support structures during the build process, which have to be removed during post-processing. Also, AM professional should decide on the optimal build orientation, which determines the strength of the part. For plastic, there are two AM processes, SLS and FDM. SLS can produce slightly stronger parts, but is also more expensive. Therefore, the decision tree is constructed in such a way that when both processes are possible, FDM is preferred. Figure 3.3 shows a simplified version of the decision tree, the complete version can be found in Appendix D.

3.3.2 Decision tree metal In a similar way, a decision tree for metal parts is developed. This is shown in Figure 3.4. Here, we make no difference between AM processes such as SLS and EBM, because their capabilities are very similar. This decision tree is designed around the characteristics of the printable materials. A selection of three materials is made. Aluminum is suitable for parts with low demand on strength, it is light, relatively cheap and has an excellent thermal conductivity. Titanium is both light and strong, and thus a very good multipurpose material. Inconel is a good replacement for stainless steel, and can be used under very high operating temperatures, which is necessary for engine parts.

When a metal part is printed, post processing may be required to reach the desired part properties, such as surface roughness. Heat treatment can be used to decrease internal stresses in a metal part. Post processing may also be required to reach the final shape, such as small holes in the part. The amount of post processing can become very large, and can influence the cost effectiveness of AM. Because post processing is part specific, we cannot capture this in the decision tree. Also, certain post processing techniques for metal parts may not be available for AM.

3.3.3 Conclusion AM suitability model Figure 3.3 and 3.4 are implemented into an application, that can be used by TC. A screenshot of the application can be found in Appendix B. This application has been reviewed with engineers of TC, who conclude that this is a tool that can be used to quickly assess AM feasibility of parts. However, the engineers also conclude that expert knowledge on the application of the part is still needed to determine printability. For metal parts, this expert knowledge is more important, given that a wider range of applications and possible post processing techniques is needed. Because of the large number of post processing techniques, it is not possible to capture this is in a decision tree structure.

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Figure 3.3: Decision tree plastic; values not indicated are in mm

13

Figure 3.4: Decision tree metal; values not indicated are in mm

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Additive Manufacturing costs In this chapter, we answer Research Question 2: What are the costs of producing with AM? AM costs can be split over multiple costs factors, which are discussed in Section 4.1. In Section 4.2 we discuss how costs can be allocated to a part based on machine time, and in Section 4.3 we validate the model.

AM cost factors The total cost per part of AM, đ?‘‡đ??ś can be divided into fixed development costs (đ??šđ??ś), direct variable costs (đ??ˇđ?‘‰), and indirect variable costs (đ??źđ?‘‰). The total costs can be described with Equation 4.1: đ?‘‡đ??ś = đ??šđ??ś + đ??ˇđ?‘‰ + đ??źđ?‘‰

(4.1)

In Figure 4.1 we show the costs factors that we use to calculate the AM costs for a single part. The fixed costs are allocated to a part based on the total expected production volume, the indirect variable costs based on the time a part needs on the AM machine. This time includes set-up, build, and cool down time.

Figure 4.1: AM costs for aviation

Figure 4.1 is an adaptation of Ruffo et al. (2006). Compared with Ruffo et al., we add post processing to the direct costs. This is a factor that is ignored by Ruffo et al., because they focus on relatively simple plastic parts, where post processing is not important. However, for production parts, post processing can significantly increase the part costs, depending on the amount of post processing needed.

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The fixed development costs are also ignored by Ruffo et al., because they focus solely on production costs. For TC, the development costs include certification and engineering to prepare a part for AM. This can become a significant factor, and is therefore included in this cost model. Finally, Ruffo et al. specified a great number of detailed overhead costs such as energy, hardware, and software; we simplified these into one overhead cost factor.

In Chapter 5 and 6, we use the model developed in this chapter to calculate the production costs for AM. In these chapters, we do not include the fixed development costs in the per part production costs. The development costs are treated separately. Furthermore, the production costs are increased with a markup factor for outsourcing production. This results in the total variable production costs as shown in Equation 4.2, for which we use the variables in Table 4.1: Table 4.1: Variables AM production costs

Variable ���� � �� ��

Notation Variable AM production costs Markup factor Indirect variable costs Direct variable costs

Assumption 0.2 Equation 4.4 Equation 4.5

đ??śđ?‘ƒđ??´đ?‘€ = (1 + đ?‘€) ∗ (đ??źđ?‘‰ + đ??ˇđ?‘‰)

(4.2)

In this chapter, we use đ?‘Ľ to indicate an AM process in the set of AM processes, and đ?‘Ś to indicate an AM material in the set of AM materials: Table 4.2: Set of machines and materials

AM machine đ?’™ FDM SLS SLM

AM material đ?’š Ultem PA12 PA12FR (Flame Retardant) PEEK Aluminum Stainless steel Titanium Inconel

4.1.1 Direct variable costs As shown in Figure 4.1, the direct variable costs (đ??ˇđ?‘‰) consist of material, material waste and the amount of post processing. For these cost factors, a set of inputs and assumptions is needed to calculate the direct costs. These are shown in Table 4.3 and 4.4.

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Table 4.3: Direct cost assumptions

Factor Notation Part volume đ?‘‰ Support material waste for đ?‘Šđ?‘Ľđ?‘ đ?‘š process đ?’™ đ?‘?

Powder waste for process đ?’™ đ?‘Šđ?‘Ľ Build time đ?‘‡đ??ľ Post processing for process đ?’™ đ?‘ƒđ?‘ƒđ?‘Ľ Labor costs post processing đ??żđ?‘ƒđ?‘ƒ đ?‘€đ??śđ?‘Ś Material cost material đ?’š

Assumption {25%, 0%, 25%} of part volume {0%, 2.5%, 2,5%} of building box Equation 4.7 {10%, 10%, 20%} of build time â‚Ź50/hour Table 4.4

Table 4.3 shows that for the different AM processes different amounts of waste material are created.

Support structures are needed for both FDM and SLM processes. In the SLS process, the plastic powder already functions as support (Materialise, 2016). The amount of support structures for FDM and SLM is highly variable with the shape of the part that is being built. Therefore, there is not one correct number that can represent the total support structure. We assume the support structure is dependent on the total build volume, which means the bigger the part, the more support material is needed.

Figure 4.2 shows a typical part with support structures in red. We assume that support material in this figure is about 25% of the part volume. In simple parts, the support percentage may be close to 0% of the part volume, but for very complex parts, the support percentage can be over 100% in extreme cases (estimation based on Strano et al. (2012). In our cost model, we assume a factor of 25% as an average waste factor. We do realize that there can be a significant deviation from this factor, and therefore we make an analysis in Chapter 6, to see whether or not this factor significantly influences the part price.

Figure 4.2: Support material metal AM (Materialise, 2016))

In the powder bed fusion processes, (SLS and SLM), additional waste is created from the unused powder.

During the process the unused powder can decrease in quality, and can therefore not be re-used indefinitely. After each production run the powder should be sewed, and can then be mixed with new powder. The mixing ratio determines how much powder waste is created. Ruffo et al. state that for Duraform material in SLS the maximum recycling percentage is 67% of the building box, which is the smallest box that can encapsulate a part. Given that often only a small percentage of the building box is used for production, this means that huge amounts of waste are created. Other sources state that only a

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very small fraction of waste is created (Peeters, 2016), or that material can be reused indefinitely (Saunders, 2016). Given these different sources, we assume a waste percentage of 2,5% of the unused powder. In the case studies in Chapter 6 we analyze if this waste factor is a significant factor in the total price of an AM part. We can calculate the amount of powder waste according to Equation 4.3: đ?‘?

đ?‘ƒđ?‘œđ?‘¤đ?‘‘đ?‘’đ?‘&#x; đ?‘¤đ?‘Žđ?‘ đ?‘Ąđ?‘’ = (đ?‘‹đ?‘Œđ?‘? − đ?‘‰) ∗ đ?‘Šđ?‘Ľ

(4.3)

Here, đ?‘‹, đ?‘Œ and đ?‘? are the dimensions of the smallest box that can encapsulate the part. From this volume, we subtract the volume đ?‘‰ of the part, because this share of the powder is used in the process. What remains is the unused powder, which is multiplied with the corresponding powder waste factor, đ?‘Šđ?‘Ľđ?‘ƒ , with đ?‘Ľ ∈ {đ??šđ??ˇđ?‘€, đ?‘†đ??żđ?‘†, đ?‘†đ??żđ?‘€}.

In Table 4.4 the machine and material prices are shown. The material prices are provided by EOS (2015).

The machine prices are estimates based on an interview at Materialise (2016). The prices shown are typical values, but there are machines available at both lower and higher costs.

Table 4.4: Machine and material prices

Machine x FDM SLS Metal AM

Machine price (₏) Material y ��� 200,000* Ultem PA12 400,000* PA12FR (Flame Retardant) PEEK 800,000* Aluminum Stainless steel Titanium Inconel

Material cost/cm3 (â‚Ź) đ?‘´đ?‘Şđ?’š 0.48 0.10* 0.10 0.37 0.30 0.76 1.94 1.94* *assumed values

For both PA12 and Inconel, we have not found material prices. Therefore, we assume values based on comparable materials. We assume PA12 has approximately the same price as PA12FR, and Inconel the same as titanium. With the inputs from Table 4.3 and Table 4.4, the direct variable costs of producing a part of material đ?‘Ś with machine đ?‘Ľ can be calculated according to Equation 4.4: đ?‘?

đ??ˇđ?‘‰ = (đ?‘‰ ∗ (1 + đ?‘Šđ?‘Ľđ?‘ đ?‘š ) + (đ?‘‹đ?‘Œđ?‘? − đ?‘‰) ∗ đ?‘Šđ?‘Ľ ) ∗ đ?‘€đ??śđ?‘Ś + đ?‘‡ đ??ľ ∗ đ?‘ƒđ?‘ƒđ?‘Ľ ∗ đ??żđ?‘ƒđ?‘ƒ

(4.4)

4.1.2 Indirect variable costs The indirect variable costs (đ??źđ?‘‰) are calculated based on the machine time. This time is used to calculate how much of the machine price, machine maintenance and overhead is allocated to a certain part. As explained, we also use the build time to calculate the amount of post processing needed. In order to calculate these costs, we need a set of assumptions, which are shown in Table 4.5.

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Table 4.5: Indirect machine costs

Factor Machine time Build time Machine price for machine đ?’™ Machine lifetime Machine utilization Machine maintenance Overhead

Notation đ?‘‡đ?‘€ đ?‘‡đ??ľ đ?‘€đ?‘ƒđ?‘Ľ đ??żđ?‘‡ đ?‘ˆ đ?‘€đ??´ đ?‘‚

Assumption Section 4.2 Section 4.2 Table 4.4 8 years 5,000 hours/year 5% of machine price / year â‚Ź10,000/year

With the assumptions of Table 4.5, the indirect cost based on the machine time can be calculated according to Equation 4.5: đ??źđ?‘‰

(� � )

đ?‘‡đ?‘€ đ?‘€đ?‘ƒđ?‘Ľ = ∗ ((1 + đ?‘€đ??´) ∗ + đ?‘‚) đ?‘ˆ đ??żđ?‘‡

(4.5)

Table 4.5 shows both machine and build time. The first variable is the time a part needs on the machine, including heat up and cool down time. The build time is the time needed to print the volume of the part.

In the next section we show how the machine time đ?‘‡ đ?‘€ and build time đ?‘‡ đ??ľ can be estimated.

Machine and build time calculation The process time determines which part of the indirect costs is allocated over the parts produced. This process time consists of three parts: the heat up phase of the machine, the build time, and the cool down phase. The heat up and cool down is a fixed time per build. In this build, multiple parts can be made, therefore the heat up and cool down time have to be distributed over all these parts. The heat up and cool down times are different for each of the AM processes, Kellens et al. (2011) and Gibson et al. (2015) state a heat up and cool down time for SLS of 4 hours. We assume this takes longer for metal AM, because of the higher temperatures needed, and shorter for FDM. Furthermore, the building chamber volumes are different between the AM processes. This is shown in Table 4.6: Table 4.6: Machine characteristics

Process đ?’™ FDM SLS SLM

Volume building chamber 3 đ?‘˝đ?’ƒđ?’„ đ?’™ (cm ) 729,000 (90*90*90) 180,000 (90*40*50) 64,000 (40*40*40)

Heat up + cool down time (hours) đ?‘Żđ?‘Şđ?’™ 3 4 5

We distribute the heat up and cool down time based on the relative volume the part needs in the building chamber. The volume the part needs is đ?‘‰đ?‘?đ?‘œđ?‘Ľ , the smallest box that can encapsulate the part. The relative volume a part needs in AM process đ?‘Ľ is: đ?‘…đ?‘Łđ?‘Ľ =

đ?‘‰đ?‘?đ?‘œđ?‘Ľ đ?‘‰đ?‘Ľđ?‘?đ?‘?

(4.6)

We assume that the building speed is a simple rate of volume per time unit. This is a simplification because the real building speed depends not only on the volume, but also on the part height, part orientation and

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geometrical complexity. The build speed listed by AM manufacturers is often too optimistic. For example, SLM solutions lists a build speed of 55 cm3/hour for their metal AM machine. The same system is in use at the Direct Manufacturing Research Center (DMRC) of the university of Paderborn, and they list a maximum build speed of 25 cm3/hour.

For laser sintered plastic parts the building speed is higher than for metals, and producing plastic parts with FDM is about 25-75% faster than SLS (DMRC, 2016). For instance, DMRC (2016) also states that the FDM material Ultem can be produced with a speed of 61 cm3/h. We assume this is the same for other FDM materials. Given the 25-70% difference between FDM and SLS the corresponding volume rate of SLS is approximately 40 cm3/h (50% difference).

For metal AM, it is not possible to generalize the building speed over all materials, because of the bigger difference in thermal properties of metals compared to plastics. These thermal properties determine how much energy is needed to melt the powder, which is directly related to the building speed. EOS, a manufacturer of AM machines, lists building speeds for a number of AM metals, which together with the assumptions on FDM and SLS building speed is summarized in Table 4.7.

Table 4.7: Building speed

Material đ?’š Ultem PA12 PA12 FR PEEK Aluminum Titanium Stainless steel Inconel

Volume rate (cm3/h) ��� 61 61 40 40 26.6 18 7.2 7.2

With the inputs of Table 4.7, the build time can be calculated with the following equation: đ?‘‡đ??ľ =

� ���

(4.7)

The machine time is the build time plus the allocated heat up and cool down time based on the relative volume (as calculated in Equation 4.6) in the building chamber: đ?‘‡ đ?‘€ = đ?‘‡ đ??ľ + đ?‘…đ?‘‰đ?‘Ľ ∗ đ??ťđ??śđ?‘Ľ

(4.8)

The build time and machine time are needed in Equation 4.4 to calculate the indirect variable costs. The total costs are the sum of direct fixed, direct variable, and indirect variable costs. In case AM is outsourced, a markup on the total cost is added. We assume a markup percentage of 20%, which is also used by Abbink (2015).

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Validation The cost and build time parameters have been implemented in an Excel sheet that uses equations 4.1 – 4.8. A screenshot of this application can be found in Appendix D. In this application, the user has to define the approximate part volume, the building box parameters, the AM process, material and expected demand. The output gives the user not only the total price, but also which factors are responsible for which part of the price. The user is able to redefine input parameters, such as building speed, when the technology improves. This model is used in Chapter 6, where we make business cases for producing parts with AM. Unfortunately, we do not have real life cases to validate the model, however we can make a comparison with an estimation of Roland Berger strategy consultants (2014). This source is used by Sterkman (2014), in his research at TC, to make an initial estimate of AM production costs. Roland Berger estimates the production costs of 1 cm3 stainless steel at €3.14. Table 4.8 shows the output of our model.

Table 4.8: AM costs of 1 cm3 stainless steel

Cost factor Material Material waste Machine Machine maintenance Post processing Overhead Total

€/cm3 0.76 0.24 3.48 1.39 1.74 0.35 7.95

Total (including 20% markup)

9.54

Table 4.8 shows a significant deviation from the €3.14 by Roland Berger Strategy Consultants. There are a number of sources for this deviation. First of all, the model of Roland Berger does not consider material waste. A second source is found in post processing, which is a cost factor that is ignored by Roland Berger.

Other sources for the deviation are the machine costs, this is due to a higher utilization (57% vs. 83%) and lower machine price (€500,000 vs. €800,000). The utilization rate of 57% is based on Ruffo et al., who state that it is very hard to reach a utilization over 60%. The difference in machine price can be explained as the difference between a mid-range machine and a less expensive model. High-end machines can be bought for prices up to €1,800,000. From the values in Table 4.7, material waste and post processing are the two cost factors for which we made a general estimate, but stated that these factors are highly dependent on the part produced.

At the end of this project, further validation of the model is done in a session with industry experts. Even though this model is an improvement over the model by Roland Berger, the conclusion is that the model developed in this thesis overestimates material waste, and underestimates post-processing costs. These costs are difficult to generalize, because they are very dependent on the part geometry and application.

This is further discussed in the recommendations in Section 7.2.

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Spare parts acquisition after end of production This chapter answers Research Question 3: What is the cost optimal decision when considering multiple options for spare parts acquisition of nearly obsolete parts?

In this chapter, we consider three options for spare parts acquisition during the EOL of a part. The model is intended for nearly obsolete parts, for which it is possible to make a last time buy. The other options for spare parts acquisition are the second-hand spot market (SH), and additive manufacturing. We start with a description of the model and assumptions in Section 5.1. After that, we develop equations to evaluate the model in Section 5.2. In Section 5.3 we show how to find a near optimal solution, which can be any combination of the three options. Section 5.4 shows how this model relates to other LTB models, and in Section 5.5 we reflect on the assumptions made in this model.

Last time buy model From the options considered, the LTB is only possible at the EOP of the part, the other options can be used during the remaining service time of the aircraft. A possible strategy is to make the LTB deliberately smaller, to avoid large holding costs, and thus to fulfill the demand in the final years of the EOL via the second-hand market or AM. This strategy is shown in Figure 5.1. Other strategies where no LTB, or a very large LTB is done are also possible.

Figure 5.1: EOL strategy

5.1.1 General assumptions In this last time buy model, we assume a single stock point. After the last time buy, the inventory is reviewed periodically. Whenever inventory falls below the base stock level, a continuous review control policy is employed for the second-hand market or additive manufacturing. The model uses the following decision variables: � ��� (�) ��� (�)

Last time buy quantity Base stock level for second-hand market in period đ?‘Ą Base stock level for AM production in period đ?‘Ą.

The decision variable đ?‘†đ?‘†đ??ť and đ?‘†đ??´đ?‘€ are time-dependent, because we assume that both demand and SH supply can change during the EOL. We use the following stochastic variables to model demand and supply: đ?‘Ť(đ?’•) đ?‘şđ?‘ˇ(đ?’•)

Demand during period đ?‘Ą; demand follows a Poisson process with rate đ?œ†đ??ˇ (đ?‘Ą) Supply of SH parts during period đ?‘Ą; supply follows a Poisson process with rate đ?œ†đ?‘†đ?‘ƒ (đ?‘Ą)

The demand for spare parts is related to the installed base size of the companies’ aircraft. Because these aircraft are in their EOL, the installed base size declines, and so does the demand for spare parts. This is a demand pattern that is typical for many EOL capital goods. Supply of parts on the second-hand market comes from scrapped aircraft or unused inventories from aircraft operators. This supply becomes available

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when aircraft are taken out of service, and is thus correlated with the demand for spare parts. When an aircraft is scrapped, the parts become available on the spot market. In this thesis, we have not researched the correlation between demand, installed base size, and the second-hand supply. This can be part of future research, and we further comment on this in Section 7.2.

Figure 5.2 shows the model with the decision variables. After an initial decision on the LTB quantity đ?‘Ś, the inventory decreases until it reaches the level đ?‘†đ?‘†đ??ť (đ?œ?đ?‘†đ??ť ). At this point in time, đ?œ?đ?‘†đ??ť , a new decision has to be made, either to start with a base stock strategy for SH, or to wait until đ?‘†đ??´đ?‘€ is reached at time đ?œ?đ??´đ?‘€ , and to start a base stock strategy for AM. The SH strategy can still result in AM when the SH supply is not sufficient to fulfill all demands.

Figure 5.2: LTB model

The model in Figure 5.2 consists of two phases. In the first phase until đ?œ?đ?‘Ľ , with đ?‘Ľ ∈ {đ?‘†đ??ť, đ??´đ?‘€}, the demand is fulfilled from the on-hand inventory, and no replacement parts are bought. In the second phase, from period đ?œ?đ?‘Ľ , a base stock policy is employed. When a demand occurs, the demand is fulfilled from the onhand inventory, and a replacement parts is bought, depending on the strategy, from the second-hand market, or from an AM service provider. AM parts are bought at an AM service provider, which is assumed to have infinity capacity, and short lead times. Therefore, backordering is allowed with the AM strategy when demands cannot be fulfilled from the on-hand inventory.

With the SH strategy, the supply is limited, and the lead times are relatively long. Supply becomes available at the beginning of each period through a Poisson process, and during each period demands occur, also via a Poisson process. Demands are fulfilled from the on-hand inventory, and a replacement part is bought from the second-hand market. It is possible that the demand is larger than the second-hand market supply.

When this is the case, it is not possible to order a replacement part, which means the inventory position, which is defined as the sum of on-hand inventory and the pipeline orders, decreases. When the inventory position falls below zero, shortages towards customers occur. Due to service obligations towards customers, all demands need to be fulfilled, and AM is needed to fulfill the remaining demand of that respective period. In the next period, new SH supply becomes available, and this supply can again be used to fulfill demand. With all strategies, we assume there are no disposal costs, or remaining value for the remaining inventory.

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In the model, we assume that the variable costs of LTB parts are lower than the variable part costs of SH or AM parts. Because of this assumption, it does not make sense to buy more SH or AM parts in the first period. Furthermore, đ?‘†đ?‘†đ??ť (1) needs to be higher than đ?‘†đ??´đ?‘€ (1), because the second-hand market has a limited supply, and therefore needs a safety stock buffer. Because of these relations, we can distinguish the following two situations for the LTB model: đ?‘Ś ≼ đ?‘†đ?‘†đ??ť (đ?‘Ą) ≼ đ?‘†đ??´đ?‘€ (đ?‘Ą)

(1)

đ?‘†đ?‘†đ??ť (đ?‘Ą) ≼ đ?‘Ś ≼ đ?‘†đ??´đ?‘€ (đ?‘Ą)

(2)

The difference between situation 1 and situation two is the base stock level for the second-hand market.

Normally, we expect this to be lower than the LTB quantity, however, in some cases, SH can be very unattractive, for example due to a low supply. This would lead to a situation with a very large đ?‘†đ?‘†đ??ť , which means that also the LTB should be large. Because we are looking for the optimal LTB quantity, there should be the possibility to bypass the second-hand market in second situation, and only consider the LTB and AM. In this chapter, we focus on situation 1. In section 5.3.2 we shortly discuss situation 2, which is a simplified version of the model for situation 1.

5.1.2 Second-hand market assumptions For the second-hand market, we assume that SH parts have the same mechanical properties as normal parts. Due to service obligations, all demands need to fulfilled. In the model, this means that whenever a shortage occurs in a period, AM is needed to cover the demand. In practice there can be situations where a shortage occurs in period đ?‘Ą, but sufficient supply becomes available in period đ?‘Ą + 1. We have not included this possibility in the model, and use the following approximation instead: Approximation 1: There is no possibility to cover a shortage in period đ??­ with surplus supply from period đ??­+đ?&#x;?

The result of Approximation 1 is that all demand needs to be fulfilled within one period. When AM is needed in a period, AM development costs apply. In the next period, SH supply is again used to fulfill demands, and AM is used in the case of shortages. This is a limitation of this model, because the model assumes that when in period đ?œ?đ?‘†đ??ť a strategy for SH is used, it will continue to use this strategy, even when AM is already developed due to a shortage in a period. In case AM is used once, the development costs are already spent, and therefore it may be better to continue using only AM.

5.1.3 Additive manufacturing assumptions The production of AM will be outsourced to an AM service provider. Abbink (2015) develops a model that evaluates the cost for this situation. In this model a base stock policy is used for AM. We add a one-time fixed cost for developing the AM option, which includes the engineering work to prepare for AM and to do the certification process. Other assumptions on AM are: • •

AM parts have the same mechanical properties as normal parts AM capacity is infinite because it is outsourced

We can use the assumption that AM parts have the same mechanical properties as normal parts, because it is a prerequisite for using AM in aviation. When AM parts have lower mechanical properties as normal parts, they will not be allowed to be used in aircraft by the aviation authorities.

24

Evaluation Sections 5.2.1 -5.2.3 show how to find the costs of each of the options separately. In these sections, we focus on the situation where we consider all three options. In case there is no SH supply, we can use an adapted version of the model, which is described in Section 5.3.2.

5.2.1 Last time buy The costs for the last time buy consist of purchasing and holding costs. We have to calculate the LTB holding costs on the domain [đ?‘Ą = 1, đ?œ?đ?‘†đ??ť ], where đ?œ?đ?‘†đ??ť is the period in which the base stock level for đ?‘†đ??ť is reached. đ?œ?đ?‘†đ??ť depends on the size of the LTB, the base stock level đ?‘†đ?‘†đ??ť (đ?‘Ą), and the demand rate. When the demand follows a stable Poisson distribution, the LTB holding time, or time from 0 until the moment that 1

đ?‘†đ?‘†đ??ť (đ?‘Ą) is reached, follows an Erlang distribution with parameters đ?‘› = (đ?‘Ś − đ?‘†đ?‘†đ??ť (đ?‘Ą)) and đ?‘? = đ?œ†. However, in our model, the demand distribution is not stable, and therefore we cannot use the Erlang distribution as a distribution for the LTB holding time. As alternative, we use the following approximation: Approximation 2: We discretize the probability that the LTB inventory reaches đ?‘şđ?‘şđ?‘Ż (đ?’•) in a period đ?’•, instead of the exact moment within period đ?’• The effect of Approximation 2 is, that when đ?œ?đ?‘†đ??ť = đ?‘Ą, there is a possibility that we undershoot the demand in period đ?‘Ą. This is because đ?œ?đ?‘†đ??ť can happen at any point in time in period t. When we start a new policy for SH in period t + 1, the model skips the demand that can occur between point đ?œ?đ?‘†đ??ť and the beginning of period t + 1. In order to minimize this effect, the length of a period should be short, for example such that the expected demand in the first period equals 1.

We call the probability that the LTB inventory reaches đ?‘†đ?‘†đ??ť (đ?‘Ą) in period đ?‘Ą, the runout probability in period đ?‘Ą. The runout probabilities are calculated with Equation 5.1, for which the variables are explained in Table 5.1.

Table 5.1: Variables runout probabilities

Variable đ?’• đ?‘Ť(đ?’•) đ?‘Ť(đ?&#x;?, đ?’•)

Description Periods, � = 1,2, ‌ , � Expected demand in period � �

∑

đ??ˇ(đ?‘˘) đ?‘˘=1

đ?’š đ?‘şđ?‘şđ?‘Ż (đ?’•) đ??‰đ?‘şđ?‘Ż

LTB quantity Base stock level for SH in period đ?‘Ą Period in which the LTB inventory falls below đ?‘†đ?‘†đ??ť (đ?‘Ą)

đ?‘ƒ(đ?œ?đ?‘†đ??ť = đ?‘Ą) = đ?‘ƒ (đ??ˇ(1, đ?‘Ą) ≼ (đ?‘Ś − đ?‘†đ?‘†đ??ť (đ?‘Ą))) − đ?‘ƒ (đ??ˇ(1, đ?‘Ą − 1) ≼ (đ?‘Ś − đ?‘†đ?‘†đ??ť (đ?‘Ą − 1)))

(5.1)

When đ?‘†đ?‘†đ??ť declines between period đ?‘Ą − 1 and đ?‘Ą, there is a possibility that Equation 5.1 results in a negative value for đ?‘ƒ(đ?œ?đ?‘†đ??ť = đ?‘Ą). This happens when the base stock declines disproportionally to the extra demand in period đ?‘Ą. The base stock is determined with a service level approach based on expected remaining demand.

The expected remaining demand in period đ?‘Ą − 1 is always larger than the expected remaining demand in period đ?‘Ą. Due to this property, the base stock level in period đ?‘Ą − 1 will include a higher safety factor. This should ensure that Equation 5.1 does not result in negative values. Whenever a negative value occurs, the

25

base stock level in period đ?‘Ą should be raised to the point where Equation 5.1 results in a positive probability.

When we find with Equation 5.1 that đ?œ?đ?‘†đ??ť = đ?‘Ą, we calculate the LTB holding costs in the periods [1, đ?‘Ą], to do this, we use the following approximation: Approximation 3: We assume a linear decline in LTB inventory to calculate LTB holding costs Because we are dealing with an end-of-life situation, the demand is expected to decline in the future due to a decreased installed base. This means that most of the demand will be in the first periods, so using a linear approximation is an overestimation of the actual inventory.

We need Approximation 3 because our solution method is based on calculating runout probabilities for each period and for all possible values for the LTB quantity. With a total of đ?‘‡ periods, and a maximum LTB quantity đ?‘Śđ?‘šđ?‘Žđ?‘Ľ , this means we calculate đ?‘‡ ∗ đ?‘Śđ?‘šđ?‘Žđ?‘Ľ runout probabilities. For all of these combinations of đ?‘Ś and đ?‘Ą, different LTB holding costs apply. It is infeasible to make an estimation of actual holding costs, for each combination. This is because if we condition on the event that đ?œ?đ?‘†đ??ť = đ?‘Ą, the following equation must hold for the demand sequence that determines the inventory holding costs in periods [1, đ?‘Ą]: đ?‘Ą

∑ đ??ˇ(đ?‘˘) ≼ đ?‘Ś − đ?‘†đ?‘†đ??ť (đ?‘Ą)

(5.2)

�=1

Because đ??ˇ(đ?‘˘) is a realization of a random Poisson variable, there are many combinations of đ??ˇ(đ?‘˘) under which Equation 5.2 holds. All these combinations lead to a different value of the LTB inventory in the periods [1, đ?‘Ą], and thus to different values of LTB holding costs. Determining the expected inventory holding costs by evaluating all possible demand sequences under which Equation 5.2 holds, is infeasible, and therefore, we use a linear approximation instead. In Chapter 6 we analyze whether or not this approximation significantly influences the last buy decision.

With the assumption of linear decline in inventory, and the probability đ?‘ƒ(đ?œ?đ?‘†đ??ť = đ?‘Ą), the expected costs of an LTB of đ?‘Ś units can be calculated with Equation 5.3. The variables in this equation are explained in Table 5.2: Table 5.2: Variables LTB costs

Notation đ?‘Şđ?‘łđ?‘ťđ?‘Š (đ?’š) đ?‘Şđ?‘ˇđ?‘łđ?‘ťđ?‘Š đ?’‰ đ?‘şđ?‘şđ?‘Ż (đ?’•) đ??‰đ?‘şđ?‘Ż

Variable Expected LTB costs in periods [1, đ?œ?đ?‘Ľ ] for given đ?‘Ś Variable purchasing cost for LTB parts Holding costs factor per period Base stock level for đ?‘†đ??ť in period đ?‘Ą Period in which the LTB inventory falls below đ?‘†đ?‘†đ??ť (đ?‘Ą)

The first part of Equation 5.3 shows the direct purchasing costs for đ?‘Ś units with a variable cost of đ??śđ?‘ƒđ??żđ?‘‡đ??ľ .

The second part calculates the holding costs until the base stock đ?‘†đ?‘Ľ (đ?‘Ą) is reached for đ?‘Ľ ∈ {đ?‘†đ??ť, đ??´đ?‘€}. The final parts show the holding costs if the LTB does not reach the inventory level đ?‘†đ?‘Ľ (đ?‘‡) before đ?‘‡.

26

�

đ?‘Ś + đ?‘†đ?‘†đ??ť (đ?‘Ą) đ??¸[đ??śđ??żđ?‘‡đ??ľ (đ?‘Ś)] = đ??śđ?‘ƒđ??żđ?‘‡đ??ľ ∗ đ?‘Ś + đ??śđ?‘ƒđ??żđ?‘‡đ??ľ ∗ â„Ž ∗ ∑ đ?‘Ą ∗ ( ) ∗ đ?‘ƒ(đ?œ?đ?‘†đ??ť = đ?‘Ą) 2 đ?‘Ą=1

đ?‘Śâˆ’đ?‘†đ?‘†đ??ť (đ?‘‡)

+đ??śđ?‘ƒđ??żđ?‘‡đ??ľ ∗ â„Ž ∗ đ?‘‡ ∗

∑ đ?‘–=0

1 (đ?‘Ś − đ?‘–) ∗ đ?‘ƒ ((đ??ˇ(1, đ?‘‡)) = đ?‘–) 2

(5.3)

5.2.2 Base stock policy evaluation This section shows how to evaluate the base stock policy. This is the policy that is used from the period after which the LTB inventory falls through the base stock level for SH or AM. Due to changing demand and supply, the base stock level can change over time. With the base stock level for each period đ?‘Ą, we can calculate the expected inventory on hand, and expected backorders due to the supply lead time. For this, we use the following approximation: Approximation 4: The system immediately reaches the steady state after updating the base stock level In reality, a base stock policy will reach a steady state only when the system is observed over longer time.

Over short times, the actual inventory may be slightly higher or lower than calculated with equations 5.4 and 5.5. Because we assume short period lengths, and regularly update the base stock level, the effect of Approximation 4 is more significant than when the period length is longer. Furthermore, an extra effect can occur when the supply lead time becomes larger than the period length. Due to this, the calculations of on-hand inventory and expected backorders may differ from reality. We have not been able to quantify these effects, and recommend to further research this.

We calculate the expected on-hand inventory and expected backorders for a base stock level đ?‘†đ?‘Ľ (đ?‘Ą), Poisson demand đ??ˇ(đ?‘Ą) and supply lead time đ?‘™đ?‘Ľ with Equations 5.4 and 5.5 where đ?‘Ľ ∈ {đ?‘†đ??ť, đ??´đ?‘€} (Van Houtum & Kranenburg, 2015). đ??¸[đ?‘‚đ??ť(đ?‘Ą)] = ∑

�� (�) �=1

[đ?‘ƒ(đ??ˇ(đ?‘Ą) ∗ đ?‘™đ?‘Ľ = đ?‘†đ?‘Ľ (đ?‘Ą) − đ?‘˘) ∗ đ?‘˘]

đ??¸[đ??ľđ?‘‚(đ?‘Ą)] = đ??ˇ(đ?‘Ą) ∗ đ?‘™đ?‘Ľ − đ?‘†đ?‘Ľ (đ?‘Ą) + ∑

�� (�) �=0

[đ?‘ƒ(đ??ˇ(đ?‘Ą) ∗ đ?‘™ = đ?‘˘) ∗ (đ?‘†đ?‘Ľ (đ?‘Ą) − đ?‘˘)]

(5.4) (5.5)

5.2.3 Second-hand market This section evaluates the costs of using the second-hand market. Before we can evaluate these costs, we need to determine the base stock level for each period. The base stock has to fulfill multiple criteria. First of all, the minimum value for the base stock can be determined with a newsvendor solution, where the probability that the base stock level exceeds the demand during lead time, is bigger than, or equal to, the critical ratio of backorder and holding costs (Van Houtum & Kranenburg, 2015) . đ?‘ƒ(đ?‘†đ?‘†đ??ť ≼ đ??ˇ(đ?‘Ą) ∗ đ?‘™) ≼

đ?‘? đ?‘?+â„Ž

(5.6)

However, the base stock should also buffer against the uncertain supply of parts. A backorder due to the limited supply exists when (đ??ˇ(đ?‘Ą) − đ?‘†đ?‘ƒ(đ?‘Ą)) > đ?‘†đ?‘†đ??ť (đ?‘Ą). In those cases, AM needs to be developed to fulfill the remaining demand. We can model the difference between demand and supply with the Skellam distribution (Skellam, 1943). The Skellam distribution is the discrete probability function for the difference between two Poisson distributed variables. Other variables are introduced in Table 5.3.

27

Table 5.3: Variables Skellam distribution

{‌ − 1,0,1, ‌ } Difference between the realizations of đ??ˇ(đ?‘Ą) and đ?‘†đ?‘ƒ(đ?‘Ą) Expected Poisson distributed demand and supply in period đ?‘Ą Modified Bessel function Gamma distribution function

đ?’Œ đ?‘˛ đ?‘Ť(đ?’•), đ?‘şđ?‘ˇ(đ?’•) đ?‘°đ?’Œ (đ?’›) đ?šŞ

The probability density function of the Skellam distribution is given by: đ?‘˜

đ?‘ƒ(đ??ž = đ?‘˜) = đ?‘’

−(đ??ˇ(đ?‘Ą)+đ?‘†đ?‘ƒ(đ?‘Ą))

đ??ˇ(đ?‘Ą) 2 ( ) đ??źđ?‘˜ (2√đ??ˇ(đ?‘Ą)đ?‘†đ?‘ƒ(đ?‘Ą)) đ?‘†đ?‘ƒ(đ?‘Ą)

(5.7)

In Equation 5.7, đ??źđ?‘˜ (đ?‘§) is the modified Bessel function, which is given by: ∞

đ??źđ?‘˜ (đ?‘§) = ∑ đ?‘š=0

1 đ?‘§ 2đ?‘š+đ?‘˜ ( ) đ?‘š! Γ(đ?‘š + đ?‘˜ + 1) 2

(5.8)

In Equation 5.8, we use the absolute value for the difference đ?‘˜, i.e. đ??źđ?‘˜ (đ?‘§) = đ??ź|đ?‘˜| (đ?‘§). Next to the newsvendor condition of Equation 5.6, the base stock level should be sufficient to buffer against supply shortages. This is done according to Equations 5.9 -5.11. In these equations, we need the notation shown in Table 5.4.

Table 5.4: Variables base stock calculations

�� ��(�) ��(�, �)

Risk factor ∈ [0,1] Expected supply of SH parts in period đ?‘Ą đ?‘‡

∑

đ?‘†đ?‘ƒ(đ?‘˘) đ?‘˘=đ?‘Ą

We want to avoid shortages, and the extra costs related to developing AM, and therefore we introduce a risk factor đ?‘…đ??š. The risk factor đ?‘…đ??š, should be determined based on the costs related to a shortage, i.e. when the costs of a shortage are high, the risk factor should be low. In this thesis, however, we determine đ?‘…đ??š arbitrarily, and set it to a value of 0.05. This is a conservative factor, because we know the costs of developing AM are high. In Section 7.2 we recommend to further research the optimal value for đ?‘…đ??š depending on the costs of developing AM. In Equation 5.9, we ensure that the probability that the sum of the base stock level and supply within a period is smaller than the demand, is smaller than the risk factor. đ?‘ƒ(đ?‘†đ?‘†đ??ť (đ?‘Ą) + đ?‘†đ?‘ƒ(đ?‘Ą) ≤ đ??ˇ(đ?‘Ą)) ≤ đ?‘…đ??š

28

(5.9)

The probabilities in Equation 5.9 can be found with the cumulative density function of the Skellam distribution. For the periods đ?œ?đ?‘†đ??ť + 1, đ?œ?đ?‘†đ??ť + 2, ‌ , đ?‘‡, we can use Equation 5.9 to update the base stock level each period.

With Equation 5.9, the shortage risk over multiple periods can still become large. Therefore, we also need to consider the cumulative shortage risk based on the expected future demand and supply: đ?‘ƒ (đ?‘†đ?‘†đ??ť (đ?‘Ą) + đ?‘†đ?‘ƒ(đ?‘Ą, đ?‘‡) ≤ (đ??ˇ(đ?‘Ą, đ?‘‡))) ≤ đ?‘…đ??š

(5.10)

This condition calculates the shortage risk based on the cumulative demand and cumulative supply from period đ?‘Ą to đ?‘‡. Finally, we set the following restriction for the base stock: đ?‘†đ?‘†đ??ť (đ?‘Ą) ≼ đ?‘†đ?‘†đ??ť (đ?‘Ą + 1)

â&#x2C6;&#x20AC;đ?&#x2018;Ą < đ?&#x2018;&#x2021;

(5.11)

With this restriction, the base stock is decreasing over time. This is a logical assumption, because in practice, the expected remaining demand declines over time. When the second-hand market does not decrease drastically over time, the base stock can decline over time while retaining the same high service level. A mathematical reason that we use this restriction, is that there is a risk in increasing the base stock between two periods. Increasing the base stock creates additional demand, which increases the risk of having a shortage in supply. Due to the restriction on the decreasing base stock, we have to start with determining the base stock in the final period, and work backwards towards the first period.

Once we have determined the base stock levels, we can calculate total SH costs. This consists of the following components: â&#x20AC;˘ â&#x20AC;˘ â&#x20AC;˘

Purchasing costs Holding costs Shortage costs due to SH supply shortages

We find the purchasing costs by using the expected demand. However, we have to adjust the demand because we are updating the base stock level. When we update the base stock level between two consecutive periods, we do not discard these parts. Instead, the base stock will be updated through a demand in the next period, which will not trigger an order for a replacement item. This means that if a strategy for SH is started in period đ?&#x2018;Ą, we do not have to order đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;&#x2021;) items. We can find the total expected SH ordering costs in the period đ?&#x2018;Ą, đ?&#x2018;&#x2021; with Equation 5.12, for which the variables are introduced in Table 5.5: Table 5.5: Variables SH purchasing

Notation đ?&#x2018;Ź[đ?&#x2018;Şđ?&#x2018;śđ?&#x2018;şđ?&#x2018;Ż (đ?&#x2019;&#x2022;, đ?&#x2018;ť)] đ?&#x2018;Şđ?&#x2018;ˇđ?&#x2018;şđ?&#x2018;Ż đ?&#x2018;Ť(đ?&#x2019;&#x2022;) đ?&#x2018;şđ?&#x2018;şđ?&#x2018;Ż (đ?&#x2019;&#x2022;)

Variable Expected SH ordering costs from period đ?&#x2018;Ą to đ?&#x2018;&#x2021;.

Variable SH costs Expected demand in period đ?&#x2018;Ą SH base stock level in period đ?&#x2018;Ą đ?&#x2018;&#x2021;

đ??¸[đ??śđ?&#x2018;&#x201A;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = đ??śđ?&#x2018;&#x192;đ?&#x2018;&#x2020;đ??ť â&#x2C6;&#x2014; ((â&#x2C6;&#x2018; đ??ˇ(đ?&#x2018;˘)) â&#x2C6;&#x2019; (đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;&#x2021;)))

(5.12)

đ?&#x2018;˘=đ?&#x2018;Ą

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The expected on-hand inventory can be found with the standard equation which is shown in Equation 5.4.

The shortage costs due to limited supply consist of two components, the fixed development costs of AM, and the extra variable costs for AM production. Therefore, we need to know the risk of a shortage, and the expected number of shortages. The risk of shortages, due to limited supply from period đ?&#x2018;Ą to đ?&#x2018;&#x2021;, đ?&#x2018;&#x2020;đ?&#x2018;&#x2026;(đ?&#x2018;Ą, đ?&#x2018;&#x2021;), can be calculated with Equation 5.13: đ?&#x2018;&#x2020;đ?&#x2018;&#x2026;(đ?&#x2018;Ą, đ?&#x2018;&#x2021;) = 1 â&#x2C6;&#x2019; [đ?&#x2018;&#x192;(đ??ˇ(đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x192;(đ?&#x2018;Ą) < đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą)) â&#x2C6;&#x2014; đ?&#x2018;&#x192;(đ??ˇ(đ?&#x2018;Ą + 1) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x192;(đ?&#x2018;Ą + 1) < đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą + 1)) â&#x2C6;&#x2014; â&#x20AC;Ś â&#x2C6;&#x2014; đ?&#x2018;&#x192;(đ??ˇ(đ?&#x2018;&#x2021;) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x192;(đ?&#x2018;&#x2021;) < đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;&#x2021;))]

(5.13)

We evaluate Equation 5.13 with the cumulative Skellam distribution. With the probability density function of the Skellam distribution, we can calculate the probability that the difference đ??ž between supply and demand is đ?&#x2018;&#x2DC;, with đ?&#x2018;&#x2DC; = [0,1,2, â&#x20AC;Ś ). With that probability, we find the expected shortages with Equation 5.14: đ?&#x2018;&#x2021;

đ??¸[đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2020; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = â&#x2C6;&#x2018;

â&#x2C6;&#x17E;

â&#x2C6;&#x2018;

(đ?&#x2018;&#x2DC; â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;˘)) â&#x2C6;&#x2014; đ?&#x2018;&#x192;(đ??ž = đ?&#x2018;&#x2DC;)

(5.14)

đ?&#x2018;˘=đ?&#x2018;Ą đ?&#x2018;&#x2DC;=đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;˘)+1

For these parts, we have to pay the variable AM costs instead of the variable SH costs, which results in the total expected shortage costs that can be found with Equation 5.15. For this equation, we introduce the notation shown in Table 5.6: Table 5.6: Variables SH shortage costs

đ?&#x2018;şđ?&#x2018;Ş(đ?&#x2019;&#x2022;, đ?&#x2018;ť) đ?&#x2018;şđ?&#x2018;š(đ?&#x2019;&#x2022;, đ?&#x2018;ť) đ?&#x2018;Şđ?&#x2018;Ťđ?&#x2018;¨đ?&#x2018;´ đ?&#x2018;Şđ?&#x2018;ˇđ?&#x2018;¨đ?&#x2018;´ đ?&#x2018;Şđ?&#x2018;ˇđ?&#x2018;şđ?&#x2018;Ż

Shortage costs from period t through T The risk that a shortage occurs in periods t through T Fixed AM costs Variable AM costs Variable SH costs đ??¸[đ?&#x2018;&#x2020;đ??ś(đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = đ?&#x2018;&#x2020;đ?&#x2018;&#x2026;(đ?&#x2018;Ą, đ?&#x2018;&#x2021;) â&#x2C6;&#x2014; đ??śđ??ˇđ??´đ?&#x2018;&#x20AC; + đ??¸[đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2020; ] â&#x2C6;&#x2014; (đ??śđ?&#x2018;&#x192;đ??´đ?&#x2018;&#x20AC; â&#x2C6;&#x2019; đ??śđ?&#x2018;&#x192;đ?&#x2018;&#x2020;đ??ť )

(5.15)

The total expected costs for using the second-hand market in periods [đ?&#x2018;Ą, đ?&#x2018;&#x2021;], đ??¸[đ??śđ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)], can be found with Equation 5.16: đ?&#x2018;&#x2021;

đ??¸[đ??śđ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = â&#x2C6;&#x2018;(đ??śđ?&#x2018;&#x192;đ?&#x2018;&#x2020;đ??ť â&#x2C6;&#x2014; đ??¸[đ??ˇ(đ?&#x2018;˘)] + â&#x201E;&#x17D; â&#x2C6;&#x2014; đ??¸[đ?&#x2018;&#x201A;đ??ť(đ?&#x2018;˘)]) đ?&#x2018;˘=đ?&#x2018;Ą

+đ??¸[đ?&#x2018;&#x2020;đ??ś(đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] â&#x2C6;&#x2019; (đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;&#x2021;)) â&#x2C6;&#x2014; đ??śđ?&#x2018;&#x192;đ?&#x2018;&#x2020;đ??ť

(5.16)

Equation 5.16 first shows the purchasing costs for the remaining expected demand. Next to that, there are holding costs. After that, the expected shortage costs are added. Finally, we correct the purchasing costs for the declining base stock level, as explained with Equation 5.12.

30

5.2.4 Additive manufacturing In the situation where đ?&#x2018;Ś â&#x2030;Ľ đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť â&#x2030;Ľ đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; , we need to make a decision on the best strategy for the remaining periods if the LTB inventory is decreased to đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť . This happens in period đ?&#x153;?đ?&#x2018;&#x2020;đ??ť , and a new strategy is started in period đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1. If we choose an AM strategy from period đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, the AM costs consist of three components. On the domain [đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, đ?&#x153;?đ??´đ?&#x2018;&#x20AC; ] holding cost apply for the LTB. On the domain [đ?&#x153;?đ??´đ?&#x2018;&#x20AC; + 1, đ?&#x2018;&#x2021;], we have AM production, holding and backorder costs. The third component is the LTB holding costs on the domain [đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, đ?&#x2018;&#x2021;], in case đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;&#x2021;) is not reached before đ?&#x2018;&#x2021;.

We assume that AM capacity is infinite, and thus can calculate the optimal base stock level for AM, đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; , with the critical ratio as shown in Equation 5.6. With Equations 5.4 and 5.5 we calculate the expected inventory on hand and expected backorders. Also for AM, the base stock can change over time due to changing demand. However, because we assume infinite production capacity, low demand volumes and a short supply lead time, this effect will be much smaller than with SH. In Equation 5.17 -5.20 we show the AM cost on the interval [đ?&#x2018;Ą, đ?&#x2018;&#x2021;], which we can condition on the event that đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą â&#x2C6;&#x2019; 1. When đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą â&#x2C6;&#x2019; 1, đ?&#x153;?đ??´đ?&#x2018;&#x20AC; can take the values đ?&#x2018;Ą â&#x2C6;&#x2019; 1, đ?&#x2018;Ą, â&#x20AC;Ś , đ?&#x2018;&#x2021;. Whenever đ?&#x153;?đ??´đ?&#x2018;&#x20AC; is bigger than đ?&#x153;?đ?&#x2018;&#x2020;đ??ť , LTB holding costs apply on the interval [đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, đ?&#x153;?đ??´đ?&#x2018;&#x20AC; ]. As shown in Figure 5.3, these holding costs are evaluated with Equation 5.19. There is a probability that đ?&#x153;?đ??´đ?&#x2018;&#x20AC; is not reached before đ?&#x2018;&#x2021;. The expected holding costs for that case can be found with Equation 5.20.

Figure 5.3: AM costs

Figure 5.3 shows that Equation 5.17 describes the expected costs for the AM strategy from đ?&#x153;?đ??´đ?&#x2018;&#x20AC; + 1 to đ?&#x2018;&#x2021;.

However, to compare the AM strategy with the SH strategy, we need to condition đ?&#x153;?đ??´đ?&#x2018;&#x20AC; on the event that đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą. This is shown in Equation 5.18. Starting the AM strategy at đ?&#x153;?đ??´đ?&#x2018;&#x20AC; + 1 means that LTB holding costs apply from đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1 until đ?&#x153;?đ??´đ?&#x2018;&#x20AC; .

31

In Equations 5.17-5.20 we need the notation as shown in Table 5.7: Table 5.7: Variables AM costs

đ?&#x2018;Şđ?&#x2019;&#x2018;đ?&#x2019;&#x201C;đ?&#x2018;¨đ?&#x2018;´ (đ?&#x2019;&#x2022;, đ?&#x2018;ť) đ?&#x2018;Şđ?&#x2018;¨đ?&#x2018;´ (đ?&#x2019;&#x2022;, đ?&#x2018;ť) đ?&#x2018;Şđ?&#x2018;Ťđ?&#x2018;¨đ?&#x2018;´ đ?&#x2018;Şđ?&#x2018;ˇđ?&#x2018;¨đ?&#x2018;´ đ?&#x2018;Şđ?&#x2018;Żđ?&#x2018;łđ?&#x2018;ťđ?&#x2018;Š (đ?&#x2019;&#x2022;, đ?&#x2019;&#x2013;) đ?&#x2018;Şđ?&#x2018;Żđ?&#x2018;łđ?&#x2018;ťđ?&#x2018;Š (đ?&#x2019;&#x2022;, đ?&#x2018;ť) đ?&#x2018;Şđ?&#x2018;šđ?&#x2018;¨đ?&#x2018;´ (đ?&#x2019;&#x2022;, đ?&#x2018;ť)

AM costs from đ?&#x153;?đ??´đ?&#x2018;&#x20AC; + 1 to đ?&#x2018;&#x2021; AM costs from đ?&#x153;?đ?&#x2018;&#x2020;đ??ť to đ?&#x2018;&#x2021; Fixed development costs for AM Variable AM costs LTB holding costs between đ?&#x153;?đ?&#x2018;&#x2020;đ??ť and đ?&#x153;?đ??´đ?&#x2018;&#x20AC; LTB holding costs if đ?&#x153;?đ??´đ?&#x2018;&#x20AC; is not reached before đ?&#x2018;&#x2021; Total remaining costs for the AM strategy if đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą â&#x2C6;&#x2019; 1

Equation 5.17 shows the AM costs from đ?&#x2018;Ą to đ?&#x2018;&#x2021; given that đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;Ą â&#x2C6;&#x2019; 1: đ?&#x2018;&#x2021;

đ??¸[đ??śđ?&#x2018;?đ?&#x2018;&#x;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = đ??śđ??ˇđ??´đ?&#x2018;&#x20AC; + â&#x2C6;&#x2018; đ??śđ?&#x2018;&#x192;đ??´đ?&#x2018;&#x20AC; â&#x2C6;&#x2014; đ??¸(đ??ˇ(đ?&#x2018;˘)) + â&#x201E;&#x17D; â&#x2C6;&#x2014; đ??¸[đ?&#x2018;&#x201A;đ??ť(đ?&#x2018;˘)] + đ?&#x2018;? â&#x2C6;&#x2014; đ??¸[đ??ľđ?&#x2018;&#x201A;(đ?&#x2018;˘)]

(5.17)

đ?&#x2018;˘=đ?&#x2018;Ą

As explained, we are interested in the costs for using AM from period đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, because in this period, we should be able to make a decision on which supply option is the cheapest. Equation 5.18 shows the AM costs conditioned on đ?&#x153;?đ?&#x2018;&#x2020;đ??ť . đ?&#x2018;&#x2021;

đ??¸[đ??śđ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = â&#x2C6;&#x2018; đ??śđ?&#x2018;?đ?&#x2018;&#x;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘ + 1, đ?&#x2018;&#x2021;) â&#x2C6;&#x2014; đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;˘|đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą)

(5.18)

đ?&#x2018;˘=đ?&#x2018;Ą

We find đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;˘|đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą) in the same way as we found the runout probabilities for the LTB, which is explained in Equation 5.18a: đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;˘|đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą) = đ?&#x2018;&#x192; (đ??ˇ(đ?&#x2018;Ą, đ?&#x2018;˘) â&#x2030;Ľ (đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘))) â&#x2C6;&#x2019; đ?&#x2018;&#x192; (đ??ˇ(đ?&#x2018;Ą, đ?&#x2018;˘ â&#x2C6;&#x2019; 1) â&#x2030;Ľ (đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą â&#x2C6;&#x2019; 1) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘ â&#x2C6;&#x2019; 1))) (5.18đ?&#x2018;&#x17D;) with đ?&#x2018;˘ â&#x2C6;&#x2C6; {đ?&#x2018;Ą + 1, đ?&#x2018;Ą + 2, â&#x20AC;Ś , đ?&#x2018;&#x2021;}. It is also possible that đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x153;?đ?&#x2018;&#x2020;đ??ť , for instance when đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) = đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą), we find this probability according to Equation 5.18b: đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;Ą|đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą) = đ?&#x2018;&#x192; (đ??ˇ(đ?&#x2018;Ą) â&#x2030;Ľ (đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘)))

(5.18đ?&#x2018;?)

If an AM strategy is started at đ?&#x2018;Ą = đ?&#x153;?đ??´đ?&#x2018;&#x20AC; + 1, holding cost for the LTB apply on the interval [đ?&#x153;?đ?&#x2018;&#x2020;đ??ť + 1, đ?&#x153;?đ??´đ?&#x2018;&#x20AC; ], the time between the moment that the inventory is decreased from đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť to đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; . These holding costs can be found with Equation 5.19.

32

đ?&#x2018;&#x2021;â&#x2C6;&#x2019;1

đ??¸[đ??śđ??ťđ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ą, đ?&#x2018;˘)] = đ??śđ?&#x2018;&#x192;đ??żđ?&#x2018;&#x2021;đ??ľ â&#x2C6;&#x2014; â&#x201E;&#x17D; â&#x2C6;&#x2014; â&#x2C6;&#x2018; ( đ?&#x2018;˘=đ?&#x2018;Ą

(đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘)) + đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;˘)) â&#x2C6;&#x2014; (đ?&#x2018;˘ â&#x2C6;&#x2019; đ?&#x2018;Ą) 2

â&#x2C6;&#x2014; đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;˘|đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą)

(5.19)

If we choose for an AM strategy at đ?&#x2018;Ą, there is a probability that the inventory is not decreased to đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; before đ?&#x2018;&#x2021;. In this case, holding costs for the LTB apply, which can be found with Equation 5.20: 1 (đ?&#x2018;&#x2021; â&#x2C6;&#x2019; đ?&#x2018;Ą) â&#x2C6;&#x2014; ((đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą â&#x2C6;&#x2019; 1) â&#x2C6;&#x2019; đ?&#x2018;Ľ) + đ?&#x2018;Ľ) 2 đ??¸[đ??śđ??ťđ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = đ??śđ?&#x2018;&#x192;đ??żđ?&#x2018;&#x2021;đ??ľ â&#x2C6;&#x2014; â&#x201E;&#x17D; â&#x2C6;&#x2014; â&#x2C6;&#x2018; đ?&#x2018;Ľ=0 â&#x2C6;&#x2014; đ?&#x2018;&#x192;((đ??ˇ(đ?&#x2018;Ą, đ?&#x2018;&#x2021;)) = đ?&#x2018;Ľ) đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą)

(5.20)

The total remaining cost đ??śđ?&#x2018;&#x2026;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;) of using an AM strategy given that đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť is reached in period đ?&#x2018;Ą â&#x2C6;&#x2019; 1, is the sum of Equations 5.18-5.20: đ??¸[đ??śđ?&#x2018;&#x2026;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] = đ??¸[đ??śđ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)] + đ??¸[đ??śđ??ťđ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ą, đ?&#x153;?đ??´đ?&#x2018;&#x20AC; )] + đ??¸[đ??śđ??ťđ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)]

(5.21)

Optimization In the previous sections, we have seen how the supply options can be evaluated. Now we need to determine how to find the optimal combination of these options. In this, we make a distinction between a situation with and without considering SH.

5.3.1 LTB+SH+AM We find the total expected costs for a given LTB quantity đ?&#x2018;Ś, by calculating the LTB costs, the probability that the LTB runs out in period đ?&#x2018;Ą, and the minimum remaining costs from period đ?&#x2018;Ą + 1.

The minimum remaining costs in the period [đ?&#x2018;Ą, đ?&#x2018;&#x2021;] can be found in Equation 5.22, which is the minimum of Equations 5.16 and 5.21: đ??¸[đ?&#x2018;&#x2026;min (đ?&#x2018;Ą)] = min{đ??¸[đ??śđ?&#x2018;&#x2026;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)], đ??¸[đ??śđ?&#x2018;&#x2026;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą, đ?&#x2018;&#x2021;)]}

(5.22)

After that, we can find the expected total cost đ??¸[đ??śđ?&#x2018;&#x2021;(đ?&#x2018;Ś)] for an LTB of đ?&#x2018;Ś units with Equation 5.23: đ?&#x2018;&#x2021;â&#x2C6;&#x2019;1

đ??¸[đ??śđ?&#x2018;&#x2021;(đ?&#x2018;Ś)] = đ??¸[đ??śđ?&#x2018;&#x2021;đ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ś)] + â&#x2C6;&#x2018; đ?&#x2018;&#x192;(đ?&#x153;?đ?&#x2018;&#x2020;đ??ť = đ?&#x2018;Ą) â&#x2C6;&#x2014; đ??¸[đ?&#x2018;&#x2026;min (đ?&#x2018;Ą + 1)]

(5.23)

đ?&#x2018;Ą=1

We find the lowest cost by enumeration over đ?&#x2018;Ś. As a lower bound for đ?&#x2018;Ś we choose đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (1), because of the condition đ?&#x2018;Ś â&#x2030;Ľ đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (1), the base stock level for SH in period 1. The upper bound for đ?&#x2018;Ś is determined with Equation 5.24: đ??ˇ(1, đ?&#x2018;&#x2021;) + 4 â&#x2C6;&#x2014; â&#x2C6;&#x161;đ??ˇ(1, đ?&#x2018;&#x2021;)

(5.24)

33

Equation 5.24 ensures with approximately 99,99% that the total demand is smaller than đ?&#x2018;Śmax , based on an expected total demand of đ??ˇ(1, đ?&#x2018;&#x2021;). It makes no sense to make a last time buy larger than the total demand, and therefore we should not consider values of đ?&#x2018;Ś larger than restricted by Equation 5.24.

5.3.2 LTB+AM If we look at a situation without SH, the lowest costs can be found in a similar way. First, we determine the probabilities that the LTB is decreased to đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą) in period đ?&#x2018;Ą: đ?&#x2018;&#x192;(đ?&#x153;?đ??´đ?&#x2018;&#x20AC; = đ?&#x2018;Ą) = đ?&#x2018;&#x192; (đ??ˇ(1, đ?&#x2018;Ą) â&#x2030;Ľ (đ?&#x2018;Ś â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą))) â&#x2C6;&#x2019; đ?&#x2018;&#x192; (đ??ˇ(1, đ?&#x2018;Ą â&#x2C6;&#x2019; 1) â&#x2030;Ľ (đ?&#x2018;Ś â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;Ľ (đ?&#x2018;Ą â&#x2C6;&#x2019; 1)))

(5.25)

After that, we calculate the cost using AM from đ?&#x153;?đ??´đ?&#x2018;&#x20AC; to đ?&#x2018;&#x2021;, and find the total expected costs with: đ?&#x2018;&#x2021;â&#x2C6;&#x2019;1

đ??¸[đ??śđ?&#x2018;&#x2021;(đ?&#x2018;Ś)] = đ??¸[đ??śđ?&#x2018;&#x2021;đ??żđ?&#x2018;&#x2021;đ??ľ (đ?&#x2018;Ś)] + â&#x2C6;&#x2018; đ?&#x2018;&#x192;(đ?&#x2018;Ą = đ?&#x153;?đ??´đ?&#x2018;&#x20AC; ) â&#x2C6;&#x2014; đ??¸[đ??śđ?&#x2018;?đ?&#x2018;&#x;đ??´đ?&#x2018;&#x20AC; (đ?&#x2018;Ą + 1)]

(5.26)

đ?&#x2018;Ą=1

In this case, the lower bound for đ?&#x2018;Ś is zero, because we have infinite AM production capacity, and can use this to build up the base stock level. The upper bound can again be found with Equation 5.24.

Relation to literature As described in Section 2.4.1, the LTB model is mostly related to the work of Inderfurth and Kleber (2013), and Wullms (2014). Inderfurth and Kleber describe a similar LTB model with three production options, being the LTB, retrieving parts from dismantled systems, and an extra production run. A difference with our model is that Inderfurth and Kleber do not consider fixed costs for any of the options. Another difference is that Inderfurth and Kleber assume that all dismantled systems are returned, which means that a stock of parts builds up, from which refurbished parts can be used to fulfill demand. In our model, we assumed a spot market for this option, where supply becomes available at the beginning of a period, and disappears at the end of the period. Inderfurth and Kleber use a newsvendor approach to determine order up to levels for remanufacturing and extra production, and use a marginal cost approach to determine the LTB quantity.

The model of Wullms (2014) considers only the LTB and AM. Wullms uses a similar solution method as our model, however, he uses the assumption of steady demand. Because of this assumption, the base stock level for AM stays the same for each period. After the LTB, Wullms only considers AM, and therefore, Wullms can use the Erlang distribution to describe the time at which the LTB inventory falls through the base stock level for AM. With the Erlang distribution, Wullms can give an exact solution to the model.

The model developed in this thesis is an extension of the model from Wullms, and is similar in terms of options considered to the model of Inderfurth and Kleber. We had to make a number of approximations in our model, which leads to a solution that is not exact. In Section 5.5 we summarize the limitations in our model. For future research, it can be interesting to apply the solution method of the model from Inderfurth and Kleber to our model.

34

Model limitations In developing the LTB model, we made the assumption that the demand decreases over time. The assumption of decreasing demand had a significant influence on the development of the model, and due to this assumption, we have not found a way to give an exact solution for the model. Our model is not exact on a number of points. First of all, we have used the approximation of a linear decline in LTB inventory to determine the LTB holding costs. In the sensitivity analysis, we have seen that this assumption had a relatively small influence on the total cost, without influencing the last time buy decision. However, when demand decreases at a higher rate, the effect of a linear approximation becomes larger. In Section 5.2.1, we argued that it is possible to give an approximation of the actual LTB holding costs, but due to our solution approach, this becomes a very cumbersome task. Therefore, we recommend to research other modelling approaches, for which it is not necessary to make the approximation of linear decline in inventory.

A second effect of the non-stable demand assumption is that we could not use an exact distribution of the LTB holding time. Instead we made a discrete approximation by dividing the EOL into small time buckets.

For each of these time buckets, we had to calculate the base stock levels for SH and AM. These base stock levels are not constant, because of the changing demand and supply. On the one hand, the time buckets need to be small, to get a better approximation of the LTB holding time, but on the other hand, the time buckets should be large to observe the system over a longer time. The small time buckets can also have an effect on the modelling of the second-hand market, for instance when supply lead time becomes larger than the length of a period. We have not managed to quantify the effect of the approximations in this model, and recommend to further investigate this.

35

Business cases This chapter answers Research Question 4: Can AM be used to save costs in the case of near obsolescence?

We answer this question by analyzing parts with the results from Chapters 3, 4 and 5, which means we first make a technical evaluation, then estimate AM production costs, and finally evaluate the spare parts procurement process. We evaluate two very different parts in Section 6.1 and 6.2. These parts differ, among other things, on price, material and demand. This way, we can give an insight in the different applications of AM at TC. Section 6.3 gives a conclusion for these case studies.

Ceiling bracket This first part is a bracket that holds a beam to which the ceiling of the aircraft is attached, as is shown in Figure 6.1. This part is currently made of Ultem plastic through injection molding, but due to small production volumes the price for the part is high, and, for the same reason, the part has an increased risk of becoming obsolete. This part is chosen by TC as a demonstrator part for AM, and, therefore, included in this analysis.

Figure 6.1: Ceiling bracket

6.1.1 Part evaluation This section evaluates the part based on the models from Chapter 3 and 4. We start with the technical assessment through the decision tree of Section 3.1. Table 6.1 shows the steps we take in the decision tree. This is based on part drawings and inputs from engineers at TC. Table 6.6.1: Technical feasibility

Size (mm) Wall Thickness (mm) Tolerances (mm) Strength (MPA) Surface quality Flame retardancy Result

36

<700*380*500 >1 >0.1 <50 Less important Yes FDM Ultem

Table 6.1 shows that the part can be produced with FDM in Ultem. Based on this, and part measurements, we can calculate the expected production costs with the model of Chapter 4. This results in a production cost of â&#x201A;Ź16.62. As explained in Chapter 4, there is a markup of 20% on the production costs of AM, because the production is outsourced. This results in a cost of â&#x201A;Ź19.94. In Section 6.1.3, we make a sensitivity analysis on several parameters of the cost model, and analyze the results.

Table 6.2: Input/output cost estimation

Part characteristics Part volume đ?&#x2018;˝ (cm3) Building box X (cm) Building box Y (cm) Building box Z (cm)

15 10 5 5

Process đ?&#x2019;&#x2122; Material đ?&#x2019;&#x161;

FDM Ultem

Cost/part Material Material waste Machine Machine maintenance Post Processing Overhead Total

â&#x201A;Ź 7.20 1.80 3.37 1.35 1.56 1.35 16.62

Total + Markup

â&#x201A;Ź19.94

The costs in Table 6.2 are calculated according to Equation 4.2, which means the fixed costs for developing AM are not included. The engineering department of TC made an estimation that certifying would approximately cost 200 hours, which translates to â&#x201A;Ź20,000. From these 200 hours, 50 are recurring costs for new AM projects where the same process and material is used. For this case, we will use only the nonrecurring development costs, i.e. â&#x201A;Ź15,000. We do not include the recurring costs, because these can be spread over many other AM parts. The development costs will be included once we evaluate the LTB model. A breakdown of the certification costs can be found in Appendix E.

6.1.2 Last time buy decision This section shows the results of the last time buy model of Chapter 5. For this model, an input on demand and second-hand supply is needed. Demand prediction is not in the scope of this project; therefore, we use a simple method to estimate future demand. The trend is that the western aircraft operators phase out their aircraft earlier, whereas the low-cost country operators continue to use the aircraft for a longer period. These low-cost operators often have lower demands on parts. This means that the biggest proportion of demands is taken out of service in the earlier periods, and the part of the fleet with low demands is phased out in a later stage. This result in a demand pattern as described in Equation 6.1. đ??ˇ(đ?&#x2018;Ą) = đ??ˇ(1) â&#x2C6;&#x2014; đ?&#x2018;&#x201C; đ?&#x2018;Ąâ&#x2C6;&#x2019;1

(6.1)

Because of the assumption of declining demand, đ?&#x2018;&#x201C; can take values between 0 and 1. This simple approach is also used in a similar setting by Fortuin (1981). In this case, we set đ?&#x2018;&#x201C; at a value of 0.95, which means that the expected demand declines each year with 5%.

The prediction of SH supply is more difficult, because not all parts can be purchased on the second-hand market. The supply comes from scrapped aircraft, and unused inventories of operators. This means that the supply is strongly correlated with the rate at which aircraft are scrapped, however, we have not found a way to model this correlation. This is a point which we will further point out in the recommendations section.

37

In the case of the ceiling bracket, there is no real second-hand market supply, however, there is a manufacturer that is willing to produce the same part, but, at a much higher price. This option has the same logistical characteristics as the second-hand market, and therefore we treat this option as the second-hand market. For the AM option, we assume a fixed development costs of â&#x201A;Ź15,000.

Table 6.3: LTB model inputs

Fixed cost (â&#x201A;Ź) Variable costs (â&#x201A;Ź per part) Lead time đ?&#x2019;? (years) Supply đ?&#x2018;şđ?&#x2018;ˇ per year

LTB 750 35 â&#x2C6;&#x17E;

AM 15,000 20 0.04 â&#x2C6;&#x17E;

2nd hand 450 0.1 â&#x2C6;&#x17E;

The other input parameters for the model are shown in Table 6.4.

Table 6.4: Model parameters

Yearly expected demand at t=1 Yearly demand growth factor Planning horizon (years) Expected total demand Period length (years) Holding costs factor đ?&#x2019;&#x2030; per year Backorder costs factor đ?&#x2019;&#x192; per year

4 0.95 10 32 0.5 20% of purchase value 180% of purchase value

With the parameters of Table 6.3 and 6.4, we can calculate the base stock levels for AM and SH. Since both the AM and SH supply are unlimited, we can determine the base stock level for both options with the newsvendor solution. This results in a base stock level of 1 in each period. Running the model with these parameters results in a total cost of â&#x201A;Ź3,620 at an LTB quantity of 36. This is shown in Figure 6.1, which shows the total cost as a function of the LTB quantity.

Total expected costs as function of LTB quantity â&#x201A;Ź 18.000 â&#x201A;Ź 16.000 â&#x201A;Ź 14.000 â&#x201A;Ź 12.000 â&#x201A;Ź 10.000 â&#x201A;Ź 8.000 â&#x201A;Ź 6.000 â&#x201A;Ź 4.000 â&#x201A;Ź 2.000 â&#x201A;Ź0

Figure 6.2: LTB model bracket

38

Figure 6.2 shows that the lowest costs can be found at an LTB quantity of 36, where the total expected demand is 32. This means that, with a probability of 0.79, the demand is smaller than, or equal to the LTB quantity. If we choose an LTB quantity lower than 36, the risk of having to use the expensive alternative options becomes larger. If we choose a higher LTB quantity, the risk of buying too many parts increases, and this results in higher holding costs.

In Table 6.5 we show the evaluation of the model, with different combinations of the options.

Table 6.5: Model evaluation

LTB LTB quantity đ?&#x2019;&#x161; 41 đ?&#x2018;ˇ(đ?&#x2018;Ť â&#x2030;¤ đ?&#x2018;łđ?&#x2018;ťđ?&#x2018;Š) 0.95 Expected total 3,903 costs â&#x201A;Ź

LTB+SH 36 0.79 3,620

LTB+AM 43 0.98 4,449

LTB+SH+AM 36 0.79 3,620

AM 0 0 15,665

In the model, all demands have to be fulfilled, however, this is not possible if we only use the LTB. For this option, we set the LTB quantity such that, with a probability of 95%, the demands can be fulfilled. For this option, penalty costs have to be paid in case the demand is higher than the LTB. We set these penalty costs to a value of â&#x201A;Ź450 per backorder, which is the same as the SH variable costs. With these penalty costs, we can see the effect of making the LTB decision with and without the second-hand market.

We can see in Table 6.5 that a combination of the LTB and SH leads to the lowest costs. In this case, the probability that all demand can be fulfilled from the base stock is 0.79. The costs for an LTB with a service level of 0.95 results in a relatively small cost increase. If we consider only the LTB and AM, the costs for not fulfilling demand via the LTB are high, because we have to develop AM. Therefore, the model sets a high LTB quantity, where the probability that all demands can be fulfilled from the LTB quantity is 0.98.

The highest costs are found when we consider only AM, due to the high development costs.

In evaluating the model, we have to keep in mind that the model results in expected costs, and therefore, the solutions may not be robust. For instance, in the combination of LTB and AM, if the demand is higher than 43, AM needs to be developed. In that case the total cost increase with at least â&#x201A;Ź15,000. This is one of the points that we further research in the sensitivity analysis.

6.1.3 Sensitivity analysis It is clear that with the current AM development costs, using AM does not result in lower costs. However, the costs for developing AM are expected to decline in the future. Therefore, we make a sensitivity analysis on the AM development costs. Once we find the point at which AM results in the same costs as the LTB, we research several other model parameters, to evaluate the robustness of the model.

AM development costs Figure 6.3 shows the expected costs as function of the LTB quantity, with an AM development cost of â&#x201A;Ź2,925. At this point, the expected costs of an LTB of 36 are equal to the costs of using AM. This means that the cost-optimal decision is to either make an LTB of 36, or start with AM from the beginning. In Figure 6.3, we can see that, by making no LTB, we can avoid the fixed ordering costs of â&#x201A;Ź750 the LTB. In the first part of the graph, the costs increase, because we buy relatively expensive LTB parts, but still have a high probability that SH or AM is needed to cover the final demand. From an LTB quantity of 25 to 36,

39

this risk declines. This reduces the total expected costs, until we buy more than 36 LTB items. After this point, the LTB holding cost increase faster than the decline in expected costs related to backorders.

Total expected costs as function of LTB quantity â&#x201A;Ź 8.000 â&#x201A;Ź 7.000 â&#x201A;Ź 6.000 â&#x201A;Ź 5.000

â&#x201A;Ź 4.000 â&#x201A;Ź 3.000 â&#x201A;Ź 2.000 â&#x201A;Ź 1.000 â&#x201A;Ź0

Figure 6.3: Total costs as function of LTB quantity

The development costs of â&#x201A;Ź2,925 are a factor 5 lower than the current development costs. At the costs of â&#x201A;Ź2,925, only a very small amount of certification can be done. This value can only be reached if the certification procedure changes drastically, for instance when all parts produced with certain machine settings are certified for aviation.

Demand In this part, we focus on the situation with an AM development cost of â&#x201A;Ź2,925. We have seen that in this case, the expected costs of a strategy with an LTB of 36 and an AM strategy are equal. In this analysis, we investigate which strategy is more robust to an error in demand rate estimation, by fixing the strategy that is chosen at đ?&#x2018;Ą = 0. We vary the demand by changing the expected demand in the first period; we do not change the demand growth factor. The expected costs for the LTB and AM strategies are shown in Table 6.4: Table 6.6: Sensitivity analysis demand

Expected demand in t=1

-20%

-10%

Original

+10%

+20%

LTB 36 AM

3,599 3,457

3,502 3,521

3,587 3,586

3,948 3,650

4,526 3,714

Table 6.4 shows that if the demand is lower than expected, the total costs are relatively stable for both options. This is because the biggest proportion of the costs is related to purchasing 36 parts for the LTB, and the development costs for AM. It is interesting to see that the costs for the LTB strategy decline when demand decreases with 10%, but increase when demand decreases with 10%. This is because the LTB inventory will be higher when demand is lower, and thus, the LTB holding costs increase when demand decreases. On the other hand, the costs of shortages decrease when demand decreases. When the expected demand declines with 10%, there is a significant decline in shortage costs. However, when

40

demand declines with 20%, this effect is less strong, and the influence of the extra LTB holding costs is larger.

In case the demand is bigger than expected, the AM production can easily be scaled up, which results in slightly higher production costs. But for the LTB, this is not possible because the LTB quantity is fixed. In case the LTB runs out, either AM needs to be developed, or expensive SH parts have to be bought. With this analysis, we show that there is a risk in using the expected costs in determining the sourcing strategy.

Another way to look at the robustness of the solutions, is to make a variance analysis of the total costs.

This is shown in Table 6.7. Again, we analyze the situation where the AM development costs are €2925. In Table 6.7, we list the maximum demand for various confidence levels, and calculate the expected costs of the LTB+SH strategy, and the AM strategy.

Table 6.7: Variance analysis

Confidence level Demand LTB 36+SH (€) AM (€)

80%

90%

95%

98%

36 3,270

39 4,620

41 5,520

44 6,870

3,845

3,905

3,945

4,005

In Table 6.7, we can see that when the confidence level increases, the LTB+SH solution becomes far more expensive than the AM solution. This is due to the high SH price of €450, that has to be paid for each demand that cannot be fulfilled from the LTB. With the AM strategy, the production can easily be scaled up, with only small extra costs.

AM production costs To calculate the AM production costs, we use a generalization for the cost factors material waste and postprocessing. In reality, these factors are dependent on part geometry and the application of the part. The geometry of this part is relatively simple, with a low Z-height. Therefore, a low material waste factor is expected. Varying the material waste factor between 0 and 50% of the part volume, the total production costs of this part vary between €16.06 and €23.83. Given the high development costs, and low demand volumes, this does not have a significant impact on the last buy decision.

The post processing costs of this part are estimated at €1.56, which means that only a very limited amount of post process can be done. Possible post-processing that is applied to this part can be support material removal, or sanding of the part. The current setting for post processing is 5% of the build time, varying this parameter from 0-100% of the build time results in a total cost between €18.07 and €55.57. The latter shows a very significant deviation from the estimated part costs. With these variable costs, the total costs of the AM strategy increase from €3,586 to €4,806. With those costs, the AM strategy is far more expensive than the LTB strategy. Therefore, we conclude that post processing is a very important cost factor, that can have a significant influence on the AM costs and the sourcing strategy. In analyzing other possible AM parts, the estimated post processing costs should be further investigated.

41

LTB holding costs To calculate the LTB holding costs, we use an approximation of linear decline in inventory. This is an overestimation of the actual LTB holding costs. Based on the expected demand, the LTB holding costs at an LTB of 36 are approximately â&#x201A;Ź1,260. This is determined by calculating the LTB inventory in each period according to the expected demand. With the approximation of linear decline, the holding costs are â&#x201A;Ź1,410, which means we overestimate the holding costs with around 12%. In Table 6.8 we show the effect on the LTB quantity and expected total costs if the holding costs decline with a certain percentage.

Table 6.8: Sensitivity analysis LTB holding costs

Holding cost rate/â&#x201A;Ź/year 0.2 -5% -10% -15% -20%

LTB quantity đ?&#x2019;&#x161;â&#x2C6;&#x2014; 36 36 36 37 37

Total expected costs 3,620 3,560 3,500 3,439 3,376

From Table 6.5 we conclude that the influence of overestimating LTB holding costs is relatively small. We can see that if we reduce the LTB holding cost with 10%, the total expected costs decline with 3.3%. If we overestimated the LTB holding costs with 15%, the optimal LTB quantity increases from 36 to 37. How much we overestimate the LTB holding costs, is dependent on the demand pattern. If the demand declines fast, the overestimation becomes larger. In case the demand is stable, there is no overestimation from the method we use.

Skid The second part we analyze, is a skid which is part of the main landing gear doors. It shows up in the obsolescence prediction tool of TC, and is therefore a very relevant part to investigate. It is currently made of aluminum, but due to strength requirements the AM version needs to be made of titanium. Making this part out of titanium will be costlier than making it in aluminum, but the superior mechanical properties of titanium will make it much easier to certify as airworthy. This is a relatively large part, with a length of almost 40 cm, which means that an AM machine with a large build chamber is needed to produce the part.

Figure 6.4: Skid

42

6.2.1 Part evaluation In this section, we show if this part can be printed, and what the expected production costs are. We start with the technical assessment of this part through the decision tree of Section 3.2. Again, we use inputs from engineers and drawings at TC to analyze the part. The results are shown in Table 6.9: Table 6.9: Technical feasibility skid

Size Wall Thickness Tolerances Strength Thermal conductivity Operating temperature Advice

<400*400*400 >1 >0.1 400-1000 MPA Not required <350 SLM Titanium

The advice is to produce this part with SLM in titanium. This is different from the original material of the skid, which is aluminum. This is because the aluminum produced with AM cannot reach the desired mechanical properties.

Table 6.10 shows the estimated AM production costs of the skid. Again, the fixed development costs for this part are not included. Because this is a metal part, the costs for certification are expected to be â&#x201A;Ź30,000, which is a factor two higher than the costs for the ceiling bracket.

Table 6.10: Cost estimation skid

Part characteristics Part volume đ?&#x2018;˝ (cm3) Building box X (cm) Building box Y (cm) Building box Z (cm)

Process đ?&#x2019;&#x2122; Material đ?&#x2019;&#x161;

180 40 15 10

SLM Titanium

Cost/part Material Material waste Machine Machine maintenance Post Processing Overhead Total

â&#x201A;Ź 349.20 369.57 259.38 103.75

Total+Markup

62.50 25.94 1170.33

1404.40

6.2.2 Last time buy decision For the last time buy decision, we need an estimation of demand and second-hand supply. The expected demand in the next year is six parts per year, and is expected to decline each year with 5%. Over the planning horizon of 10 years, this results in an expected demand of 47.5 parts. The expected supply on the second-hand is stable, with a rate of four parts per year, or two per period. In Table 6.11 on page 46 we show the costs of the options. For the other model parameters, we choose the same values as for the first case, which can be found in Table 6.4.

43

Table 6.11: Inputs last time buy model

LTB 0 800

Fixed cost Variable costs Lead time đ?&#x2019;? (years) Supply at t=1

AM 30,000 1,404 0.04 â&#x2C6;&#x17E;

â&#x2C6;&#x17E;

2nd hand 1,000 0.1 2

Since the model parameters in this case are different from the parameters from the first case, the analysis of this case differs from the analysis of the first case. This already starts with determining the base stock levels.

Base stock levels To evaluate the model, we need to decide on the base stock levels for AM and SH. For AM, we use the standard newsvendor solution, which results in a base stock of 1 in each period. For SH, however, the supply is limited, and we need to follow the procedure of Section 5.2.3 to determine the base stock levels.

This results in the base stock levels displayed in Figure 6.5 on page 39.

Base stock levels skid 14

12 10 8 SH 6

AM

4 2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 Figure 6.5: Base stock levels skid

In Figure 6.5, we can see that over 20 periods, the base stock level declines from 13 to 2. The biggest decline is in the first periods, where the difference between demand and supply is the largest. In the final periods, the expected supply is larger than the expected demand, and a relatively small base stock level is sufficient to cover the supply uncertainty. Figure 6.5 also shows the base stock for AM. With this, we can clearly see one of the logistical advantages of AM. Due to the unlimited supply and short lead times, we can hold significantly lower inventory levels compared to the uncertain second-hand market.

44

If we run the model with the base stock levels displayed in Figure 6.5, and the parameters of Table 6.11, we find the expected costs as a function of the LTB quantity as displayed in Figure 6.6:

Total expected costs as function of LTB quantity

â&#x201A;Ź 110.000

â&#x201A;Ź 100.000

â&#x201A;Ź 90.000

â&#x201A;Ź 80.000

â&#x201A;Ź 70.000

â&#x201A;Ź 60.000

â&#x201A;Ź 50.000

Figure 6.6: LTB model skid

The lowest expected costs are â&#x201A;Ź78,566, at an LTB quantity of 44. With this LTB quantity, there is a probability of 68% that the LTB inventory runs out before đ?&#x2018;&#x2021;, and that either SH or AM is needed. The probabilities that the LTB inventory is decreased to đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť (đ?&#x2018;Ą) start to take higher values from period 15, which is after 7 years. This is shown in Table 6.12, where we also show the remaining costs for choosing the SH or AM strategy. It is interesting to see that the runout probabilities do not always follow the expected bell-shaped curve, for instance, the runout probabilities between period 18 and 19 decrease, but between period 19 and 20, the runout probabilities increase. This is because the base stock is changing over time.

Table 6.12: Runout probabilities for LTB = 44

Period

Runout probability in đ?&#x2019;&#x2022;

Cumulative runout probability

15 16 17 18 19 20

0.103 0.119 0.123 0.116 0.047 0.089

0.167 0.270 0.389 0.512 0.628 0.675

Expected remaining costs SH â&#x201A;Ź 23,325 18,251 13,559 9,279 6,318 2,745

Expected remaining costs AM â&#x201A;Ź 44,641 41,138 36,342 27,227 20,075 17,987

Note that these are the expected costs from time đ?&#x153;?đ?&#x2018;&#x2020;đ??ť , the moment that the LTB inventory is decreased to đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť . The AM strategy at this point in time is to wait until đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;đ??ť is decreased to đ?&#x2018;&#x2020;đ??´đ?&#x2018;&#x20AC; , and then to start with AM production. In all periods, the costs for the SH strategy are lower than the costs for the AM strategy.

The extra holding costs of the SH strategy do not outweigh the AM development costs and the difference

45

in variable costs between SH and AM. However, the relative difference between the options is smaller if the remaining time is larger. When the remaining time is longer, AM has more logistical benefits that can compensate for the fixed development costs.

The three options LTB, SH, and AM are not always available. Therefore, we show in Table 6.13 the evaluation of the model, with different combinations of the obsolescence solutions. Again, we also show the probability that the demand is smaller than the LTB quantity.

Table 6.13: Model evaluation

LTB* LTB quantity 59 đ?&#x2018;ˇ(đ?&#x2018;Ť â&#x2030;¤ đ?&#x2018;łđ?&#x2018;ťđ?&#x2018;Š) 0.95 Total expected 101,800 costs â&#x201A;Ź

LTB+SH 44 0.32 78,566

LTB+AM 49 0.62 90,305

LTB+SH+AM 44 0.32 78,566

AM 0 0 99,162

Table 6.13 shows that the lowest costs are found with the strategy combining the LTB with the secondhand market. In this strategy, the LTB quantity is low compared to the expected demand. The probability that we have to use the second-hand market is 0.95. The highest costs are found when we use the LTB, where we set the LTB quantity such that, with a probability of 0.95, the LTB is larger than the total expected demand. The costs for using only AM are comparable to this strategy, even though the development costs for AM are â&#x201A;Ź30,000, and the variable AM costs are more than twice the variable costs of the LTB. A combination of the LTB and AM already reduces the expected costs with over 10%. The lowest expected costs are found with the combination of the LTB and SH. This analysis shows that over the entire life-cycle, the costs of AM can be comparable with other obsolescence solutions, despite the high development costs. However, when a reliable second-hand market supply is available, AM will not be part of the optimal sourcing strategy.

6.2.3 Sensitivity analysis Just as for the first case, we make a sensitivity analysis on a number of factors of the model. We start with making a variance analysis on the demand. After that, we analyze the effect of changes in AM development costs, and in AM variable costs.

Demand In Table 6.14, we list the maximum demand for various confidence levels, and calculate the expected costs of the LTB+SH strategy, and the AM strategy. The costs in this table are approximations, as we do not know the exact demand distribution. In the table, we can see that the LTB+SH strategy is slightly more robust than the AM strategy. This is because the variable AM costs are higher than the variable SH costs, and due to the safety stock in the SH strategy, there is only a small risk of having to develop AM.

46

However, the LTB+SH costs contain the expected SH shortage costs. Since the shortage risk is small, the expected shortage costs are small. However, when a real shortage occurs, and AM is needed, the costs will increase dramatically.

Table 6.14: Variance analysis

Confidence level Demand Expected costs (€) LTB 44+SH Expected AM costs (€)

80%

90%

95%

98%

53 75,530

56 77,340

59 79,060

62 82,420

107,000

111,200

115,400

119,600

AM development costs The current AM development costs are expected to be €30,000. In an extreme case, we can set these costs at €0. In this case, the optimal LTB quantity is 19, and the total costs are €57,988. Again, SH is always preferred over AM, simply because the variable SH costs are lower than the variable AM costs. In case there is a shortage of SH supply, AM can be used. This only results in the extra variable costs for AM. AM variable cost Table 6.15 shows at which variable AM costs, the costs of using only AM are equal to the combination of the LTB and SH. We show this for various levels of the AM development costs. Changing the AM cost parameters also has an effect on the SH strategy, due to the lower costs associated with the risk of a shortage in supply. We can see in Table 6.15, that the LTB quantity for the SH strategy decreases if the fixed AM costs decline. In other words, when the costs of having SH supply shortages decrease, this strategy is more attractive.

Table 6.15: Sensitivity analysis variable AM costs

AM development costs € 30,000 20,000 10,000 0

AM variable costs € 982 1,135 1,225 1,173

LTB quantity SH strategy 44 41 22 19

With the model of Chapter 4, we can analyze how much the parameters of the cost model should change, in order to realize the variable costs of Table 6.15. This is shown in Table 6.16, where we list three AM cost factors, and show how much they should change in order to decrease the AM production costs to approximately €980. This is the costs where the AM strategy results in the same costs as the LTB+SH strategy.

47

Table 6.16: Sensitivity analysis AM production costs

Factor

Current value

Current part cost Updated €* parameter Powder price €1.94/cm3 1,170 €1,40/cm3 Material waste 2,5% of building 1,170 1% of building box powder box Print speed 18 cm3/h 1,170 32 cm3/h *Excluding outsourcing markup

Updated costs €* 980 1,000

part

980

With the fast developments of the AM industry, it is not unrealistic that such improvements can be made in the coming years. However, there are also other factors that influence the price of the part. One of these factors is post-processing. In the model, we calculated AM post processing time as a 10% of the build time. In this case, this results in 75 minutes of post processing at a cost of €62.50. Experts indicated that this is an underestimation of the real post processing costs, because such a part needs to undergo a large amount of post processing. If we look at a situation where the post processing time is equal to the AM production time, the costs of this part increase significantly. Without the markup for outsourcing, the price of the part increases from €1,170 to €1,700. If we would use only AM during the EOL, the total expected costs increase from €99,162 to €132,754.

Conclusion case studies The two case studies illustrate the models that follow from Chapter 3, 4, and 5. In both cases, AM is not part of the preferred sourcing strategy, due to the high costs. In the first case study, the use of AM is not limited due to the variable costs, but due to the fixed development costs. These costs have to decline significantly before the lifecycle costs of AM are comparable with the costs of an LTB. In the second case study, both the fixed and variable AM costs are too high. However, in this case we have seen that AM does have logistical benefits over the last time buy and the second-hand market. Because of the short lead times, and unlimited supply, the base stock level for AM was much lower than the base stock level for SH, but these benefits are not high enough to compensate for the extra development and variable costs. In the sensitivity analysis, we have seen that the AM solution can easily scale up production when demand is higher than expected. This can be a reason to choose for AM if the costs of this option are relatively close to costs of the other obsolescence solutions.

We also made an analysis on the AM production costs. We have seen that the factors material waste and post processing are important in determining the estimated production costs. Because these factors are case sensitive, it is not possible to make a generalization for these cost factors. Further analysis is needed to find a better way to estimate post-processing costs.

48

Conclusions and recommendations At the beginning of this thesis we formulated the following problem statement:

Is AM a solution for obsolescence problems at TC?

This chapter concludes on this problem statement in Section 7.1, and gives recommendations for further research regarding AM and obsolescence in Section 7.2.

Conclusions To answer the problem statement, we formulated the following research question:

Under what criteria can AM be a solution to obsolescence problems in the aviation industry, and how does the AM solution compare to other obsolescence solutions?

We answered this question with three models. First, we developed an AM suitability model in Chapter 3.

We have seen that AM is a flexible production technique that can produce complex geometries in various materials. The main materials that can be used are Ultem for plastic parts, and titanium for metal parts.

These materials can cover a significant share of the parts catalogue of TC. The production cost model estimates the variable costs of AM. When we compare the results of the model, the costs of an AM part are generally higher than those of conventionally produced parts. The price difference between conventional and AM parts is the biggest for metal parts, and smaller for plastic parts. The last time buy model determines the best sourcing strategy for nearly obsolete parts.

With these models, we make two case studies, one for a cheap plastic part, and the other for a more expensive metal part. In the first case, the development costs for AM are too high to become part of the sourcing strategy. With the sensitivity analysis, we find that the development costs should be reduced to a maximum of â&#x201A;Ź2,925. In that case, the LTB strategy and the AM strategy result in the same total expected costs. With these developments costs, about 30 hours can be spent on the development and certification of the AM solution. This is much less than the current estimate of 200 hours. We conclude that for this cheap part, the fixed development costs for AM are too high to be an alternative for the LTB. Since the difference between the current development costs and the break-even development costs is very large, we expect the same conclusion for all cheap parts. For these parts, AM can only compete with the LTB when demand is very large. However, in those cases it should be possible to also make use of conventional production techniques, instead of the LTB. The second part we analyze is more expensive, and has a higher demand. For this part we consider three sourcing options, the LTB, the second-hand market, and AM. With all options available, the best strategy is a combination of the LTB with the second-hand market. For the AM option, both the fixed development and production costs are too high. However, when we analyze different sourcing strategies, for instance without the second-hand market, we see that AM can reduce the total expected costs in comparison with

49

the solution of only an LTB. This is due to the high LTB quantity, and the holding costs related to this strategy.

We conclude that in case there is a reliable second-hand supply of parts, AM will not be the preferred obsolescence solution, due to the high development and variable costs. In case there is a very unreliable, or no second-hand supply, AM can be a solution to the obsolescence problem. The up-front investment with AM is lower compared to the LTB, and during the EOL period, the holding costs for AM are much lower than for the LTB. However, parts with a high demand do not tend to become obsolete. For these parts, manufacturers can make use of the economies of scale from the conventional production techniques. Due to this, AM will be the best solution to obsolescence in only a very limited number of cases. This can change when AM technology evolves, and both development and production costs decline.

This will lead to a situation where AM can be used for more parts, with lower demand volumes.

When the costs for AM decline, AM can be an interesting solution for obsolescence problems. This is something we have seen in the sensitivity analysis. Because of the capability of AM to produce on demand, we found that the costs of the AM solution are more robust to demand changes. This is an advantage compared to the LTB and the combination of the LTB and second-hand market. Especially when demand is higher than expected, or SH supply is lower than expected, the costs of an LTB+SH strategy can increase fast. With the AM strategy, the production can be scaled up, and only additional production costs apply.

However, there will always remain costs related to the development of AM parts, and therefore, AM has a higher potential for expensive parts.

Outside of the aviation industries, where certification costs may not apply, the potential for AM is higher.

Specific price differences and lead times between conventional, second-hand market and AM determine if AM reduces costs. In the two case studies we make, reducing the AM certification costs to zero, results in one positive business case for AM. In this case, the second-hand market is far more expensive than AM, and therefore, AM will be preferred. In the other case, the second-hand market is cheaper than AM. Due to the uncertain supply, extra safety stock is needed for a second hand-market strategy. The logistical benefits of AM do not outweigh the extra production costs for AM, and thus AM is not part of the preferred strategy.

Recommendations We have concluded that AM has the potential to be a solution for obsolescence problems, but at this point in time, it is too expensive compared to conventional manufacturing and second-hand supply. This is mainly due to the high development costs related to the certification process. The first step TC should take to continue with AM, is to make more in depth research on the certification process. It is important to analyze why this process takes so long, and at which steps this process can be improved. If these improvements are not sufficient, TC should set up a new certification process for AM parts. This is something that cannot be done at TC alone. Important actors in this process are the aviation authorities, and manufacturers of AM machines. The AM manufactures have to convince the aviation authorities of the quality and reproducibility of products from their machines. This should result in a situation where not each individual part is certified, but the production process is certified instead. When the process is certified, many parts can be produced without repeating the certification process for each different part.

Improving the certification process is a long-term solution. In the short term, another possibility may be to not print the part itself, but to print the tooling instead. The tooling can be, for instance, the molds for injection molding. These are very costly to produce conventionally, and it may be a cheaper solution to

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produce the tooling with AM. When the tooling is printed and not the part, the certification process is less expensive, because the qualifications for tooling are less strict than the qualifications for parts. This makes it easier to develop positive business cases for AM. To use the option of printing the tooling, TC has to research the qualifications for the tooling, and research which AM process and material can be used to produce the tooling.

With respect to the models developed in this thesis, a recommendation is to further validate and improve them. For the AM suitability model of Chapter 3, an improvement would be to research if more material properties, such as hardness, or surface roughness, can be added to the decision tree. This can lead to a more reliable prediction of technical AM feasibility.

For the production cost model of Chapter 4, the parameters post- processing and material waste have to be further analyzed, because we have seen that these can significantly influence the AM costs. In a validation session with industry experts it was indicated that the assumptions made in this thesis can lead to an underestimation of actual AM production costs. Another addition to the model would be to analyze how the part geometry influences the AM production costs.

In the LTB model, we have seen that using the second-hand market is an option that can significantly decrease the costs during the EOL. In the model, we used a Poisson distributed variable to describe the supply of SH parts on the spot-market. This supply is correlated with the rate at which aircraft are scrapped, but we have not researched what the exact correlation is. Because of the significance of the second-hand market, we recommend TC to investigate how a reliable prediction of SH supply can be given.

Another addition to the LTB model is to further investigate the determination of the SH base stock levels.

In this thesis, we used an arbitrarily determined risk factor to achieve a low probability of SH shortages.

This risk factor is not yet based on the costs related to a shortage, however, we argued that when shortage costs are high, the risk factor should be low. A possible way to model this is with a newsvendor solution, we recommend to further investigate this.

In Section 5.5 we already explained that due to the assumption of declining demand, we had to make a number of approximations in the LTB model. We have not quantified all the approximations made in this model, and therefore, we recommend to further analyze the influence of the approximations. Another option is to research a different modelling approach for the LTB model with declining demand. In this thesis, we used a solution method similar to the solution method of Wullms (2014), but it may be better to use an approach similar to Inderfurth and Kleber (2013). The recommendations on the on these models, can for instance be part of a follow-up Masterâ&#x20AC;&#x2122;s thesis project.

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Appendix A: Obsolescence solutions at TC This Appendix gives a short description of the seven obsolescence solutions named in Section 1.2.

1. The last buy is an order from the final production run of the original equipment manufacturer (OEM). At the end of the service time, TC has the risk of having either too many, or to few parts, which will result in additional costs.

2. The second-hand market is the market of parts from unused inventories, or from scrapped aircraft.

Parts from the second-hand market are considered slightly inferior to new parts, because of quality issues. Because the number of scrapped aircraft is increasing, this market is expected to grow.

3. Resourcing is finding a different manufacturer that can produce the same product. The price of resourced parts will be higher than the price of parts from regular manufacturing.

4. A Part Manufacturer Approval (PMA) is an approval to produce a part, even though TC is not the OEM. This option is more expensive, because it needs reverse engineering of the part, and legal work to get the PMA. 5. Development of a repair means that a procedure is developed to repair the part. Because of quality issues, repair is not considered the preferred option for every item.

6. Redesigning a part means that the part is produced with different materials or procedures. This option requires additional engineering costs, and extra costs due to aviation certification.

7. Redesigning the system means that a complete system of an obsolete part is redesigned. Again, the costs of this solution are higher due to additional engineering and certification costs.

The figure below shows the distribution of these obsolescence solutions at TC.

Distribution of obsolescence solutions 273 27%

Development of PMA part Development of Repair

75 7% 50 5%

328 33%

Buying on second hand/surplus market Complete re-design of the part

2 0%

283 28%

Last Time Buy from the OEM Re-sourcing from the OEM to an alternative manufacturer

From this figure, we learn that the development of a PMA part and a complete redesign of the system are done very seldom. Furthermore, a last time buy is done in only 7% of the cases. This shows that TC often reactively manages obsolescence. It is cheaper to do this proactively, before the actual obsolescence takes place. In that case a last buy can be done, or TC can already start with finding alternative solutions.

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At TC, Li et al. (2016) have researched how obsolescence can be predicted. In this project, several factors are found that indicate future obsolescence. For TC, these are smaller throughput, longer periods since the last order, longer average lead times, and steeper increases in lead times. These factors are implemented in a model that assigns risk scores to parts. TC uses this model to contact suppliers of parts with a high obsolescence risk. This gives TC the opportunity to proactively manage obsolescence, by making a last buy. In this project we do not further use the work of Li et al., but a good prediction of obsolescence can be very useful when deciding on producing a part with AM.

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Appendix B: Decision Tree AM The decision tree presented in Section 3.3 is implemented in an Excel application. A screenshot of the application is presented below.

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Appendix C: Aviation Certification The aviation industry is characterized by very strict safety regulations. The design of every aircraft needs to be authorized by responsible regulatory authorities. For aircraft built in Europe, this is the Europe Aviation Safety Agency (EASA). The equivalent of the EASA in the USA is called the Federal Aviation Agency (FAA).

The complete design of an aircraft is captured in the Type Design. As long as the aircraft meets its type design, and does not have any serious breakdowns, an aircraft is certified as airworthy. The original aircraft manufacturer is the holder of the type design, and called the Type Certificate Holder.

The Type Certificate Holder can change the design of the aircraft without approval of the authorities when the change is classified as Minor. A change is called Minor when it has no appreciable effect on the mass, balance, structural strength, reliability, operational characteristics, noise, fuel venting, exhaust emission, or other characteristics affecting the airworthiness of the product. When the change does have an effect on one or more of these characteristics, it should be qualified as Major, and has to be approved by the regulatory authorities. Not only the aircraft itself, but also the organization producing the aircraft needs to be certified. This is done by a Design Organization Approval (DOA). Organizations that design: aircraft, changes to aircraft, repairs of aircraft, or parts, should hold a DOA (EASA, 2016). Organizations producing for the aviation industry need to have a Production Organization Approval (POA). If TC decides to use AM, production will very likely be outsourced. This means that the AM service provider needs to have a POA. This certification is very relevant for our project at TC. TC is type certificate holder of the aircraft it produced, and holds a DOA and POA to make changes and repairs to large aircraft. Holding these certificates means that TC can also decide whether or not a change should be classified as Major or Minor.

When a part is produced in a different way than original, this is seen as a change to the type design. In case this change is classified as Major, the certification becomes a very costly and lengthy procedure. For successful usage of AM the change should be qualified as Minor. This means that engineers at TC need to prove that producing the part with AM has no effect on the before mentioned characteristics of the aircraft. A checklist for the Major/Minor change is provided on the next page.

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Appendix D: AM cost model

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Appendix E: certification hours ceiling bracket For the ceiling bracket a study is done within TC, which estimates the hours needed to certify the AM version of the part. This is split out in recurring and non-recurring costs. The non-recurring costs can be used for other parts as well, provided that they have the same material.

• • • • • • • • • •

ECR (Document explaining the change) Product Definition Report CP (Certification Plan) Process and Material Certification Report Loads Report Stress Report Drawings Stress Certification Report (test based – internal test) Test Plan for Fireworthiness Certification Report CRR (Compliance Record Report)

8h (RC) 40h (RC) 16h (RC) 16h (NRC for same material/proces) 16h (NRC if already available) 16h (RC) 16h (RC) 40h (RC) 24h (NRC for same material) 8h (RC)

Outsourced Cost: •

Flammability Material Test

<500€

Total Cost: • • •

Recurring engineering hours Non-recurring engineering hours: Extra costs for fireworthiness

144 56h <500€

Given the internal costs the certification procedure would cost €20.000, of which €5600 is non-recurring.

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